Review Multiple Choice Problems (From Past Warm-Ups)

Review Multiple Choice Problems (from past warm-ups)

2. A survey records many variables of interest to the researchers conducting the survey. Which of the following ch1 variables, from a survey conducted by the U.S. Postal Service, is categorical? A) county of residence B) number of people, both adults and children, living in the household C) total household income, before taxes, in 1993 D) age of respondent

During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below are the team-by-team statistics on home runs hit through Friday, June 3, 1994 (from the Columbus Dispatch Sports Section, Sunday, June 5, 1994), in the form of separate stemplots for the number of home runs by American and National League teams.

18. The median for the number of home runs for the American League teams is ch1 A) lower than that for the National League teams B) 45 C) 50 D) 57.5

19. Which of the following is a correct statement? ch1 A) The American League plot is reasonably symmetric. B) The National League plot is slightly skewed to the left C) The median number of home runs hit by American League teams was higher than that of National League teams D) All of the above

26. A consumer group surveyed the prices for a certain item in five different stores and reported the average price ch1 as $15. We visited four of the five stores and found the prices to be $10, $15, $15, and $25. Assuming that the consumer group is correct, what is the price of the item at the store that we did not visit? A) $10 B) $15 C) $20 D) $25

28. A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in ch1 thousands of dollars) for this year. For convenience, the data are ordered. 28 31 34 35 37 41 42 42 42 47 49 51 52 52 60 61 67 72 75 77

Suppose each employee in the company receives a $3000 raise for next year (each employee's salary is increased by $3000). The mean salary for the employees will A) be unchanged B) increase by $3000 C) be multiplied by $3000 D) increase by $3000

45. The interquartile range of the 20 salaries is ch1 A) $19,000 B) $19,500 C) $21,500 D) $49,000

48. In a statistics class with 136 students, the professor records how much money each student has in his or her ch1 possession during the first class of the semester. The histogram below is of the data collected.

From the histogram, which of the following is true? A) The mean is much larger than the median. B) The mean is much smaller than the median. C) The mean and median are approximately equal. D) It is impossible to compare the mean and median for these data.

8. The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a ch1 standard deviation of 10 minutes. Using the 68–95–99.7 rule, what percentage of students will complete the exam in under an hour? A) 68% B) 32% C) 16% D) 5%

15. A company produces packets of soap powder labeled “Giant Size 32 Ounces.” The actual weight of ch1 soap powder in a box has a normal distribution with a mean of 33 ounces and a standard deviation of 0.7 ounces. What proportion of packets is underweight (i.e., weighs less than 32 ounces)? A) .0764 B) .2420 C) .7580 D) .9236

23. A soft-drink machine can be regulated so that it discharges an average of  ounces per cup. If the ch1 ounces of fill are normally distributed with a standard deviation of 0.4 ounces, what value should  be set at so that 6-ounce cups will overflow only 2% of the time? A) 6.82 B) 6.00 C) 5.18 D) 5.60

25. The weight of a randomly selected can of a new soft drink is known to have a normal distribution ch1 with a mean of 8.3 ounces and a standard deviation of 0.2 ounces. The weight (in ounces) that should be stamped on the can so that only 2% of cans are underweight is A) 7.89 B) 8.71 C) 8.26 D) 8.28

12. A study found a correlation of r = –0.61 between the gender of a worker and his or her income. You may ch2 correctly conclude that A) women earn more than men on the average. B) women earn less than men on the average C) an arithmetic mistake was made. Correlation must be positive D) this is incorrect because r makes no sense here

9. A school guidance counselor examines the number of extracurricular activities of students and their grade ch2 point average. The guidance counselor says, “The evidence indicates that the correlation between the number of extracurricular activities a student participates in and his or her grade point average is close to zero.” A correct interpretation of this statement would be that A) active students tend to be students with poor grades, and vice versa B) students with good grades tend to be students that are not involved in many activities, and vice versa C) students involved in many extracurricular activities are just as likely to get good grades as bad grades. The same is true for students involved in few extracurricular activities D) involvement in many extracurricular activities and good grades go hand in hand

13. Consider the scatterplot below. ch2

According to the scatterplot, which of the following is a plausible value for the correlation coefficient between weight and MPG? A) +0.2 B) –0.9 C) +0.7 D) –1.0

27. In a statistics course a linear regression equation was computed to predict the final exam score ch2 from the score on the first test. The equation of the least-squares regression line was y = 10 + 0.9x where y represents the final exam score and x is the score on the first exam. Suppose Joe scores a 90 on the first exam. What would be the predicted value of his score on the final exam? A) 91 B) 89 C) 81 D) It cannot be determined from the information given

33. A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first ch2 year of life. He plots these averages versus the age X (in months) and decides to fit a least-squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities. r = correlation between X and Y = 0.9 J = mean of the values of X = 6.5 M = mean of the values of Y = 6.6 sJ = standard deviation of the values of X = 3.6 sM = standard deviation of the values of Y = 1.2

The slope of the least-squares line is A) 0.30 B) 0.88 C) 1.01 D) 3.0

35. In a study of 1991 model cars, a researcher found that the fraction of the variation in the price of cars that was ch2 explained by the least-squares regression on horsepower was about 0.64. For the cars in this study, the correlation between the price of the car and its horsepower was found to be positive. The actual value of the correlation is A) 0.80 B) 0.64 C) 0.41 D) not able to be determined from the information given

6. Using least-squares regression, I determine that the logarithm (base 10) of the population of a country is ch2 approximately described by the equation log(population) = –13.5 + 0.01 x (year) Based on this equation, the population of the country in the year 2000 should be about A) 6.5 B) 665 C) 2,000,000 D) 3,167,277

32. A study of the salaries of full professors at Upper Wabash Tech shows that the median salary for female ch2 professors is considerably less than the median male salary. However, further investigation shows that the median salaries for male and female full professors are about the same in every department (English, physics, etc.) of the university. This apparent contradiction is an example of A) Extrapolation B) Simpson’s Paradox C) Causation D) Correlation

20. Consider the following scatterplot. ch2

From this plot we can conclude A) that there is evidence of a modest cause-and-effect relation between X and Y with increases in X causing increases in Y B) that there is an outlier in the plot C) that there is a strongly influential point in the plot D) all of the above

34. The two-way table below categorizes suicides committed in 1983 by the gender of the victim and the method ch2 used. Method Male Female Firearms 13,959 2,641 Poison 3,148 2,469 Hanging 3,222 709 Other 1,457 690

Which of the following statements is consistent with the table? A) There is absolutely no evidence of a relation between the sex of the victim and the method of suicide used B) More women commit suicide than men C) Men display a greater tendency to use firearms to commit suicide than do women D) The correlation between method of suicide and sex of the victim is clearly positive

2. In order to assess the effects of exercise on reducing cholesterol, a researcher sampled 50 people from a local ch3 gym who exercised regularly and 50 people from the surrounding community who did not exercise regularly. They each reported to a clinic to have their cholesterol measured. The subjects were unaware of the purpose of the study, and the technician measuring the cholesterol was not aware of whether subjects exercised regularly or not. This is A) an observational study B) an experiment, but not a double-blind experiment C) a double-blind experiment D) a matched pairs experiment

5. A market research company wishes to find out whether the population of students at a university prefers ch3 brand A or brand B of instant coffee. A random sample of students is selected, and each student is asked first to try brand A and then to try brand B, or vice versa (with the order determined at random). They then indicate which brand they prefer. This is an example of A) an experiment B) an observational study, not an experiment C) stratified sampling design D) block design

8. In order to assess the opinion of students at the University of Minnesota on campus snow removal, a reporter ch3 for the student newspaper interviews the first 12 students he meets who are willing to express their opinion. The method of sampling used is A) simple random sampling B) convenience sampling C) voluntary response D) a census

13. The six people listed below are enrolled in a statistics course taught by means of television. Use the list of ch3 random digits 27102 56027 55892 33063 41842 81868 71035 09001 43367 49497 54580 81507 starting at the beginning of this list, to choose a simple random sample of three to be interviewed in detail about the quality of the course. Use the labels attached to the six names. 1. Moore 4. Goel 2. Casella 5. Jones 3. Santner 6. Klein

The sample you obtain is A) Moore, Casella, Jones B) 2, 7, 1 C) Moore, Casella, and again Casella D) any set of three names, but we must exclude Casella

14. A public opinion poll in Ohio wants to determine whether registered voters in the state approve of a measure ch3 to ban smoking in all public areas. They select a simple random sample of 50 registered voters from each county in the state and ask whether they approve or disapprove of the measure. This is an example of a A) systematic county sample B) stratified sample C) multistage sample D) simple random sample

20. A 1992 Roper poll found that 22% of Americans say that the Holocaust may not have happened. The actual ch3 question asked in the poll was: Does it seem possible or impossible to you that the Nazi extermination of the Jews never happened? Twenty-two percent responded “possible.” The results of this poll cannot be trusted because A) undercoverage is present. Obviously those people who did not survive the Holocaust could not be in the poll B) the question is worded in a confusing manner C) we do not know who conducted the poll or who paid for the results D) nonresponse is present. Many people will refuse to participate and those that do will be biased in their opinions

26. A sociologist wants to study the attitudes of American male college students toward marriage and husband- ch3 wife relations. She gives a questionnaire to 25 of the men enrolled in Sociology 101 at her college. All 25 complete and return the questionnaire. The sample in this situation is A) all men taking a comparable sociology class B) the 25 men who received and returned the questionnaire C) all the men in the Sociology 101 class D) all married men in the Sociology 101 class

47. Will a fluoride mouthwash used after brushing reduce cavities? Twenty sets of twins were used to investigate ch3 this question. One member of each set of twins used the mouthwash after each brushing; the other did not. After six months, the difference in the number of cavities of those using the mouthwash was compared with the number of cavities of those who did not use the mouthwash. This experiment uses A) random placebos B) double-blinding C) double replication D) a matched pairs design

Researchers wish to determine if a new experimental medication will reduce the symptoms of allergy sufferers without the side effect of drowsiness. To investigate this question, the researchers give the new medication to 50 adult volunteers who suffer from allergies. Forty-four of these volunteers report a significant reduction in their allergy symptoms without any drowsiness.

42. Referring to the information above, this study could be improved by ch3 A) including people who do not suffer from allergies in the study in order to represent a more diverse population B) repeating the study with only the 44 volunteers who reported a significant reduction in their allergy symptoms without any drowsiness, and giving them a higher dosage this time C) using a control group D) all of the above

43. Referring to the information above, the experimental units are ch3 A) the researchers B) the 50 adult volunteers C) the 44 volunteers who reported a significant reduction in their allergy symptoms without any drowsiness D) the 6 volunteers who did not report a significant reduction in their allergy symptoms without any drowsiness

6. Suppose we have a loaded die that gives the outcomes 1–6 according to the following probability ch4 distribution: X 1 2 3 4 5 6 P(X) 0.1 0.2 0.3 0.2 0.1 0.1

Note that for this die all outcomes are not equally likely, as they would be if the die were fair. If this die is rolled 6000 times, the number of times we get a 2 or a 3 should be about A) 1000 B) 2000 C) 3000 D) 4000

7. Suppose we roll a red die and a green die. Let A be the event that the number of spots showing on the red die ch4 is 3 or less and B be the event that the number of spots showing on the green die is more than 3. The events A and B are A) Disjoint B) Complements C) Independent D) Reciprocals

If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing each color depends on the proportion of each color among all candies made. Assume the table below gives the probability that a randomly chosen M&M has each color. Color Brown Red Yellow Green Orange Tan Probability .3 .3 ? .1 .1 .1

11. The probability of drawing a yellow candy is ch4 A) .1 B) .2 C) .3 D) impossible to determine from the information given

12. The probability that I do not draw a red candy is ch4 A) .1 B) .3 C) .7 D) .9

13. The probability that I draw neither a brown nor a green candy is ch4 A) .1 B) .3 C) .4 D) .6

17. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B are disjoint (mutually ch4 exclusive) then A) P(A and B) = 0.16 B) P(A or B) = 1.0 C) P(A and B) = 1.0 D) P(A or B) = 0.16

25. Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3. ch4 P(A or B) is A) 0.09 B) 0.51 C) 0.52 D) 0.60

An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability that both A and B will occur is 0.1. 32. Referring to the information above, the conditional probability of A given B ch4 A) is 0.3 B) is 0.2 C) is 1/6 D) cannot be determined from the information given

33. Referring to the information above, we may conclude ch4 A) that events A and B are independent B) that events A and B are disjoint C) that either A or B always occurs D) none of the above

38. The probability of a randomly selected adult having a rare disease for which a diagnostic test has been ch4 developed is 0.001. The diagnostic test is not perfect. The probability the test will be positive (indicating that the person has the disease) is 0.99 for a person with the disease and 0.02 for a person without the disease. The proportion of adults for which the test would be positive is A) 0.00099 B) 0.01998 C) 0.02097 D) 0.02100

A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music. Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability distribution: Value of X 1 2 3 4 Probability 0.2 0.4 0.3 0.1

1. Referring to the information above, the probability that a randomly chosen subject completes at least three ch4 puzzles in the five-minute period while listening to soothing music is A) 0.3 B) 0.4 C) 0.6 D) 0.9

2. Referring to the information above, P(X < 3) has value ch4 A) 0.3 B) 0.4 C) 0.6 D) 0.9

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume X is normal with a mean of $360 and standard deviation $50. 13. Referring to the information above, the value of P(X > $400) is ch4 A) 0.2881 B) 0.8450 C) 0.7881 D) 0.2119

14. Referring to the information above, the probability is approximately 0.6 that on a randomly selected day the ch4 store will make less than A) $347.40 B) $0.30 C) $361.30 D) $372.60

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1; if number of spots showing is 6 you win $4; and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. 15. Referring to the information above, the expected value of X is ch4 A) $0 B) $1 C) $2.50 D) $4

16. Referring to the information above, the variance of X is ch4 A) 1.0 B) 3/2 C) 2.0 D) 13/6

27. I toss a fair coin a large number of times. Assuming tosses are independent, which of the following is true? ch4 A) Once the number of flips is large enough (usually about 10,000) the number of heads will always be exactly half of the total number of tosses. For example, after 10,000 tosses I should have 5000 heads B) The proportion of heads will be about ½, and this proportion will tend to get closer and closer to ½ as the number of tosses increases C) As the number of tosses increases, any long run of heads will be balanced by a corresponding run of tails so that the overall proportion of heads is ½ D) All of the above

A small store keeps track of the number X of customers that make a purchase during the first hour that the store is open each day. Based on the records, X has the following probability distribution. X 0 1 2 3 4 P(X) 0.1 0.1 0.1 0.1 0.6

28. Referring to the information above, the mean number of customers that make a purchase during the first hour ch4 that the store is open is A) 2 B) 2.5 C) 3 D) 4

29. Referring to the information above, the standard deviation of the number of customers that make a purchase ch4 during the first hour that the store is open is A) 1.4 B) 2 C) 3 D) 4

30. Referring to the information above, suppose the store is open seven days a week from 8:00 AM to 5:30 PM. ch4 The mean number of customers that make a purchase during the first hour that the store is open during a one- week period is A) 3 B) 9 C) 21 D) 28

8. In a certain game of chance, your chances of winning are 0.2. If you play the game five times and outcomes ch5 are independent, the probability that you win at most once is A) 0.0819 B) 0.2 C) 0.4096 D) 0.7373

A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 40% of all adults in Ohio support the increase. 11. The mean of X is ch5 A) 5% B) 0.40 C) 40 D) 600

12. The standard deviation of X is ch5 A) 360 B) 40 C) 24.49 D) 18.97

13. The probability that X is more than 750 is ch5 A) less than 0.0001 B) about 0.1 C) 0.4602 D) 0.50 D) 0.50.

16. Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let X be ch5 the number of successes in the sample. For which value of p would it be safe to assume the distribution of X is approximately normal? A) 0.01 B) 1/9 C) 0.975 D) 0.9999

17. In a test of ESP (extrasensory perception), the experimenter looks at cards that are hidden from the subject. ch5 Each card contains either a star, a circle, a wavy line, or a square. An experimenter looks at each of 100 cards in turn, and the subject tries to read the experimenter's mind and name the shape on each. What is the probability that the subject gets more than 30 correct if the subject does not have ESP and is just guessing? A) 0.3100 B) .2500 C) 0.1251 D) less than 0.0001

24. A college basketball player makes 5/6 of his free throws. Assuming free throws are independent, the ch5 probability that he makes exactly three of his next four free throws is 3 1 A) 1 5 4       6 6 . 3 1 B) 1  5      6 6 . 1 3 C) 1 5 4   6  6  . 1 3 D) 1  5  6  6  .

27. A college basketball player makes 80% of his free throws. Over the course of the season he will attempt 100 ch5 free throws. Assuming free throw attempts are independent, the probability that the number of free throws he makes exceeds 80 is approximately A) 0.2000 B) 0.2266 C) 0.5000 D) 0.7734

33. A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free ch5 throw she attempts. The probability that she doesn't make a free throw until her fifth attempt this season is A) 0.32768 B) 0.08192 C) 0.00128 D) 0.00032

34. A college basketball player makes 80% of her free throws. Suppose this probability is the same for each free ch5 throw she attempts. The probability that she makes all of her first four free throws and then misses her fifth attempt this season is A) 0.32768 B) 0.08192 C) 0.00128 D) 0.00032

8. If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true ch5 value of the parameter being estimated, the statistic is said to be A) Random B) Biased C) A Proportion D) Unbiased

10. The variability of a statistic is described by ch5 A) the spread of its sampling distribution B) the amount of bias present C) the vagueness in the wording of the question used to collect the sample data D) the stability of the population it describes

23. A random sample of size 25 is to be taken from a population that is normally distributed with mean 60 and ch5 standard deviation 10. The average J of the observations in our sample is to be computed. The sampling distribution of J is A) normal with mean 60 and standard deviation 10 B) normal with mean 60 and standard deviation 2 C) normal with mean 60 and standard deviation 0.4 D) normal with mean 12 and standard deviation 2

27. A random variable X has mean μX and standard deviation σX. Suppose n independent observations of X are ch5 taken and the average J of these n observations is computed. We can assert that if n is very large, the sampling distribution of J is approximately normal. This assertion follows from A) the law of large numbers B) the central limit theorem C) the definition of sampling distribution D) the bell curve

32. Suppose that you are a student worker in the statistics department and they agree to pay you using the ch5 Random Pay system. Each week the chair of the department flips a coin. If it comes up heads, your pay for the week is $80; if it comes up tails, your pay for the week is $40. Your friend is working for the engineering department and makes $65 per week. The probability that your total earnings in 100 weeks are more than hers is approximately A) 0.0000 B) 0.4013 C) 0.5000 D) 0.5987

33. A researcher initially plans to take a SRS of size n from a population that has mean 80 and standard deviation ch5 20. If he were to double his sample size (to 2n), the standard deviation of the sampling distribution of J would change by a factor of A) C) 2 D) 1/2 2 B) 1/ 2

The SAT scores of entering freshmen at University X have a N(1200, 90) distribution, and the SAT scores of entering freshmen at University Y have a N(1215, 110) distribution. A random sample of 100 freshmen is sampled from each university, with J the sample mean of the 100 scores from University X 38. The probability that J is less than 1190 is ch5 A) 0.0116 B) 0.1335 C) 0.4090 D) 0.4562

6. An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the ch6 average yield for these plots is found to be 162.72  4.47 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than this 90% confidence interval? A) planting only five plots rather than 25, since five are easier to manage and control. B) planting 100 plots rather than 25. C) computing a 99% confidence interval rather than a 90% confidence interval; the increase in confidence indicates that we have a better interval. D) none of the above.

You measure the heights of a random sample of 400 high school sophomore males in a Midwestern state. The sample mean is J = 66.2 inches. Suppose that the heights of all high school sophomore males follow a normal distribution with an unknown mean and population standard deviation of 4.1 inches. 7. A 95% confidence interval for the population mean is ch6 A) (58.16, 74.24) B) (59.46, 72.94) C) (65.8, 66.6) D) (65.86, 66.54)

16. Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first ch6 year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal distribution with a population standard deviation of $30. The number of observations required is closest to A) 25 B) 30 C) 609 D) 865

17. Other things being equal, the margin of error of a confidence interval increases as ch6 A) the sample size increases B) the confidence level decreases C) the population standard deviation increases D) none of the above

24. The mean area of the several thousand apartments in a new development is advertised to be 1250 square feet. ch6 A tenant group thinks that the apartments are smaller than advertised. They hire an engineer to measure a sample of apartments to test their suspicion. The appropriate null and alternative hypotheses, H0 and Ha are A) are H0: μ = 1250, Ha: μ ≠ 1250 B) are H0: μ = 1250, Ha: μ < 1250 C) are H0: μ = 1250, Ha: μ > 1250 D) cannot be specified without knowing the sample size

26. In a test of significance, the probability, assuming the null hypothesis is true, that the test statistic will take a ch6 value at least as extreme as that actually observed is A) the P-value of the test B) the level of significance of the test C) the probability the null hypothesis is true D) the probability the null hypothesis is false

28. In a statistical test of hypotheses, we say the data are statistically significant at level α if ch6 A) α = 0.05 B) α is small C) the P-value is less than α D) the P-value is larger than α

29. In a test if statistical hypotheses, the P-value tells us ch6 A) if the null hypothesis is true B) if the alternative hypothesis is true C) the largest level of significance at which the null hypothesis can be rejected D) the smallest level of significance at which the null hypothesis can be rejected

33. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and ch6 population standard deviation = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of J = 1.53. Is this evidence that the mean nicotine content is actually higher than advertised? To answer this, test the hypotheses H0: μ = 1.5, Ha: μ > 1.5 at the 5% significance level. You conclude A) that H0 should be rejected B) that H0 should not be rejected C) that Ha should be rejected D) that there is a 5% chance that the null hypothesis is true

35. The time needed for college students to complete a certain paper-and-pencil maze follows a normal ch6 distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time μ is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. You compute the average time J that it takes these students to complete the maze and test the hypotheses H0: μ = 30, Ha: μ ≠ 30 You find that the results are significant at the 5% level. You may also conclude that the test would also A) be significant at the 10% level B) be significant at the 1% level C) both of the above D) none of the above

41. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The ch6 new bulb has a lifetime of 1201 hours, using a sample of 2000 bulbs. Although the difference is quite small, the effect was statistically significant. The explanation is A) that new designs typically have more variability than standard designs B) that the sample size is very large C) that the mean of 1200 is large D) all of the above

45. An engineer designs an improved light bulb. The previous design had an average lifetime of 1200 hours. The ch6 mean lifetime of a random sample of 2000 new bulbs is found to have a mean lifetime of 1201 hours. Although the difference from the old mean lifetime of 1200 hours is quite small, the P-value is 0.03 and the effect is statistically significant at the 0.05 level. If, in fact, there is no difference between the mean lifetimes of the new and old designs, the researcher has A) committed a type I error B) committed a type II error C) a probability of being correct that is equal to the P-value D) a probability of being correct that is equal to 1 – (P-value)

47. A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have ch6 a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a type I error is A) 0.01 B) 0.10 C) 0.90 D) equal to the p-value and cannot be determined

49. Which of the following will increase the value of the power in a statistical test of hypotheses? ch6 A) increase the significance level B) increase the sample size C) consider computing the power for a value of the alternative that is farther from the value of the parameter of interest under the null hypothesis D) all of the above

50. A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have ch6 a power of 0.90 at a particular alternative value of the parameter of interest. The probability that the researcher will commit a type II error for the particular alternative value of the parameter at which she computed the power is A) 0.01 B) 0.10 C) 0.90 D) equal to 1 – (P-value)

51. The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams)  and ch6 standard deviation μ = 0.1. The brand advertises that the mean nicotine content of its cigarettes is 1.5, but you are suspicious and plan to investigate the advertised claim by testing the hypotheses H0: μ = 1.5, Ha: μ > 1.5 at the 5% significance level. You will do so by measuring the nicotine content of 100 randomly selected cigarettes of this brand and computing the mean nicotine content J of your measurements. The power of your test at μ = 1.6 is A) 0.7995 B) 0.8413 C) 0.95 D) greater than 0.999

2. The one sample t statistic from a sample of n = 19 observations for the two-sided test of ch7 H0: μ = 6 Ha: μ ≠ 6 has the value t = 1.93. Based on this information A) we would reject the null hypothesis at α = 0.10 B) 0.025 < P-value < 0.05 C) we would reject the null hypothesis at α = 0.05 D) both (b) and (c) are correct

3. The heights (in inches) of males in the United States are believed to be normally distributed with mean . The ch7 average height of a random sample of 25 American adult males is found to be J = 69.72 inches and the standard deviation of the 25 heights is found to be s = 4.15. The standard error of J is A) 0.17 B) 0.69 C) 0.83 D) 2.04

4. Scores on the Math SAT (SAT-M) are believed to be normally distributed with mean μ. The scores of a ch7 random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for μ based on these data is A) 550.00 ± 173.88 B) 550.00 ± 142.00 C) 550.00 ± 128.58 D) 550.00 ± 105.01

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. Net weights actually vary slightly from bag to bag and are normally distributed with mean μ. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and so intends to test the hypotheses H0: μ = 14, Ha: μ < 14 To do this, he selects 16 bags of this brand at random and determines the net weight of each. He finds the sample mean to be J = 13.88 and the sample standard deviation to be s = 0.24.

10. Based on the data above, ch7 A) we would reject H0 at significance level 0.10 but not at 0.05 B) we would reject H0 at significance level 0.05 but not at 0.025 C) we would reject H0 at significance level 0.025 but not at 0.01 D) we would reject H0 at significance level 0.01

11. Referring to the information above, suppose we were not sure if the distribution of net weights was normal. ch7 In which of the following circumstances would we not be safe using a t procedure in this problem? A) The mean and median of the data are nearly equal B) A histogram of the data shows moderate skewness C) A stemplot of the data has a large outlier D) The sample standard deviation is large

21. The heights (in inches) of adult males in the United States are believed to be normally distributed with mean ch7 μ. The average height of a random sample of 25 American adult males is found to be J = 69.72 inches, and the standard deviation of the 25 heights is found to be s = 4.15. A 90% confidence interval for μ is A) 69.72 ± 1.09 B) 69.72 ± 1.37 C) 69.72 ± 1.42 D) 69.72 ± 4.15

A sports writer wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean yardage for group 1 was J1 = 30 yards with a standard deviation s1 = 8 yards. The mean yardage for group 2 was J2 = 26 yards with a standard deviation s2 = 6 yards. Assume the two groups of kicks are independent. Let μ 1 and μ 2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium- and an air-filled football.

31. Referring to the information above, assuming two sample t procedures are safe to use, a 99% confidence ch7 interval for μ 1 – μ 2 is (use the conservative value for the degrees of freedom) A) 4 ± 4.7 yards B) 4 ± 6.2 yards C) 4 ± 7.7 yards D) 4 ± 11.2 yards

32. Referring to the information above, suppose the researcher had wished to test the hypotheses ch7 H0: μ 1 = μ 2, Ha: μ 1 > μ 2 The P-value for the test is (use the conservative value for the degrees of freedom) A) larger than 0.10 B) between 0.10 and 0.05 C) between 0.05 and 0.01 D) below 0.01

33. Referring to the information above, to which of the following would it have been most important that the ch7 subjects be blind during the experiment? A) the identity of the sports writer B) the direction in which they were to kick the ball C) the method they were to use in kicking the ball D) whether the ball they were kicking was filled with helium or air

38. A researcher wished to compare the effect of two stepping heights (low and high) on heart rate in a step- ch7 aerobics workout. A collection of 50 adult volunteers was randomly divided into two groups of 25 subjects each. Group 1 did a standard step-aerobics workout at the low height. The mean heart rate at the end of the workout for the subjects in group 1 was J1 = 90.00 beats per minute with a standard deviation s1 = 9 beats per minute. Group 2 did the same workout but at the high step height. The mean heart rate at the end of the workout for the subjects in group 2 was J2 = 95.08 beats per minute with a standard deviation s2 = 12 beats per minute. Assume the two groups are independent and the data are approximately normal. Let μ 1 and μ 2 represent the mean heart rates we would observe for the entire population represented by the volunteers if all members of this population did the workout using the low or high step height, respectively. Suppose the researcher had wished to test the hypotheses H0: μ 1 = μ 2, Ha: μ 1 < μ 2 The P-value for the test is (use the conservative value for the degrees of freedom) A) larger than 0.10 B) between 0.10 and 0.05 C) between 0.05 and 0.01 D) less than 0.01

The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed along with a quote of their response are printed in the paper. Students are interviewed by a reporter “roaming” the campus who selects students to interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. Four of the students say no. The proportion p that respond “no” is thus 0.8. 1. Referring to the information above, the standard error SEp of the proportion is ch8 A) 0.8 B) 0.64 C) 0.18 D) 0.032

2. Referring to the information above, which of the following assumptions for inference about a proportion ch8 using a confidence interval are violated in this example? A) The data are an SRS from the population of interest B) The population is at least 10 times as large as the sample C) We are interested in inference about a proportion D) There appear to be no violations

A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the card was one of five symbols: star, cross, circle, square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial.

8. Referring to the information above, based on the results of the test, a 95% confidence interval for p is ch8 (assume the 400 trials can be treated as an SRS from the population of all guesses the psychic would make in his lifetime) A) 0.25 ± 0.060 B) 0.25 ± 0.055 C) 0.25 ± 0.050 D) We can assert that p = 0.20 with 100% confidence because the psychic is just guessing.

9. Referring to the information above, suppose you wished to see if there is evidence that the psychic is doing ch8 better than just guessing. To do this you test the hypotheses H0: p = 0.20, Ha: p > 0.20 The P-value is A) between .10 and .05 B) between .05 and .01 C) between .01 and .001 D) below .001

10. Referring to the information above, how large a sample n would you need to estimate p with margin of error ch8 0.01 with 95% confidence? Use the guess p = 0.20 as the value for p. A) n = 4330 B) n = 6147 C) n = 7203 D) n = 9604

22. An SRS of 100 of a certain popular model car in 1993 found that 20 had a certain minor defect in the brakes. ch8 An SRS of 400 of this model car in 1994 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1993 and 1994, respectively, that actually contain the defect. A 90% confidence interval for p1 – p2 is 0.075 ± 0.071. Suppose the sample of 1993 cars consisted of only 10 cars, of which two had the minor brake defect. Suppose also the sample of 1994 cars consisted of only 40 cars, of which five had the minor brake defect. A 90% confidence interval for p1 – p2 is now A) the same as that for the original sample of 100 and 400 cars B) much narrower than that for the original sample of 100 and 400 cars C) the same as 99% for the original sample of 100 and 400 cars D) It is unsafe to compute using the normal distribution to approximate the sampling distribution of p1 – p2

25. A manufacturer receives parts from two suppliers. An SRS of 400 parts from supplier 1 finds 20 defective. ch8 An SRS of 100 parts from supplier 2 finds 10 defective. Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that is defective. A 95% confidence interval for p1 – p2 is A) –.05 ± 0.063 B) –.05 ± 0.053 C) –.05 ± 0.032 D) .05 ± 0.032

An SRS of 25 male faculty members at a large university found that 10 felt that the university was supportive of female and minority faculty. An independent SRS of 20 female faculty found that five felt that the university was supportive of female and minority faculty. Let p1 and p2 represent the proportion of all male and female faculty, respectively, at the university who felt that the university was supportive of female and minority faculty at the time of the survey.

30. Referring to the information above, a 95% confidence interval for p1 – p2 is ch8 A) 0.15 ± 0.355 B) 0.15 ± 0.270 C) 0.15 ± 0.227 D) 0.15 ± 0.138

31. Referring to the information above, is there evidence that the proportion of male faculty members who felt ch8 the university was supportive of female and minority faculty is larger than the corresponding proportion for female faculty members? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 > p2. The P-value is A) larger than .05 B) between .05 and .01 C) between .01 and .001 D) below .001

I teach a large introductory statistics course. In the past, the proportion of students that receive a grade of A is 0.20. The proportion that receives a B is 0.30. The proportion that receives a C is 0.30. The proportion that receives a D is 0.10. The proportion that receives an F is 0.10. This year, there were 200 students in the class and I gave the following grades. A B C D F Number 56 74 60 9 1

9. I wish to test whether the distribution of grades this year is the same as in the past. To do so I plan to use the ch9 X2 statistic. We know that this X2 statistic has approximately a X 2 distribution. How many degrees of freedom does this distribution have? A) 200 B) 199 C) 5 D) 4

10. I wish to test whether the distribution of grades this year is the same as in the past. To do so I plan to use the ch9 X2 statistic. The component of this X2 statistic corresponding to a grade of C is A) (O – E)2/E = 0 B) (O – E)2/E = 1 C) (O – E)2/E = 30 D) (O – E)2/E = 11,880.3

11. I wish to test whether the distribution of grades this year is the same as in the past. To do so I use the X2 ch9 statistic and I compute its value to be 33.77. The P-value of our test is A) greater than 0.10 B) between 0.10 and 0.05 C) between 0.05 and 0.01 D) less than 0.01

12. I wish to test whether the distribution of grades this year is the same as in the past. To do so I use the X2 ch9 statistic. I may assume the X2 statistic has an approximate chi-square distribution because of which of the following? A) The expected number of people in each grade category is greater than 5 B) The sample size is 200, which is large enough for the chi-square approximation to be valid C) The number of categories is small relative to the number of observations D) I may not assume the X2 statistic has an approximate chi-square distribution because there is only one person in the F grade category

13. I wish to test whether the distribution of grades this year is the same as in the past. To do so I use the X2 ch9 statistic. The grade category that contributes the largest component to the X2 statistic is A) A B) B C) D D) F

A study was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the grades 4, 5, and 6 from schools in Georgia. The students received a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Results are presented in the table below by the sex of the child. Boys Girls Make good grades 96 295 Be popular 32 45 Be good in sports 94 40

31. Which hypotheses are being tested by the chi-square test? ch9 A) The null hypothesis is that personal goals and gender are independent and the alternative is that they are dependent B) The null hypothesis is that the mean personal goal is the same for boys and girls and the alternative is that the means differ C) The distribution of personal goals is different for boys and girls D) The distribution of gender is different for the three different personal goals

32. The numerical value of the chi-square statistic for this table is ch9 A) 3.84 B) 5.99 C) 16.015 D) 89.966

An old saying in golf is “you drive for show and you putt for dough.” The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data on the top 69 money-winners on the PGA tour in 1993 are examined. The average number of putts per hole for each player is used to predict their total winnings using the simple linear regression model 1993 winningsi = β0 + β 1(average number of putts per hole)i + ei where the deviations ei are assumed to be independent and normally distributed with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. R2 = 0.081 s = 281,777 Variable Parameter Estimate Std. Err. of Parameter Est. Constant 7,897,179 3,023,782 Avg. Putts –4,139,198 1,698,371

1. The explanatory variable in this study is ch10 A) 1993 winnings B) average number of putts per hole C) the slope, β 1 D) –4,139,198

2. The quantity s = 281,777 is an estimate of the standard deviation of the deviations in the simple linear ch10 regression model. The degrees of freedom for s are A) 69 B) 68 C) 67 D) 281,777

3. The intercept of the least-squares regression line is ch10 A) 7,897,179 B) –4,139,198 C) 3,020,782 D) 1,698,371

4. Suppose the researchers test the hypotheses H0: β 1 = 0, Ha: β 1 < 0 The value of the t statistic for this test is ch10 A) 2.61 B) 2.44 C) 0.081 D) –2.44

5. A 95% confidence interval for the slope β 1 in the simple linear regression model is (approximately) ch10 A) 7,897,179 ± 3,023,782 B) 7,897,179 ± 6,047,564 C) –4,139,198 ± 1,698,371 D) –4,139,198 ± 3,396,742

6. The correlation between 1993 winnings and average number of putts per hole is ch10 A) 0.081 B) –0.081 C) 0.285 D) –0.285