Stat 100 Final Exam Fall 2002

Stat 100 Final Exam Fall 2002 Each problem is worth 20 points. Do one problem per answer sheet. All work must be shown to receive full credit. 1. In the following cases, a linear relation was found to exist between the given variables. For each case, choose the option (i, ii, or iii) that best describes the relation. a) The GPA and the SAT scores. i) the correlation coefficient r = -.9, ii) the regression line is y = 220 + 91x, iii) the correlation coefficient r = 0 b) The body length and the weight for male wolves. i) the regression line is y = 98 - .04x, ii) the correlation coefficient r = .6, iii) the correlation coefficient r = -.8 c) The age of adults and their ability to maintain a strenuous exercise program. i) the regression line is y = 4x + 2, ii) the correlation coefficient r = .7, iii) the correlation coefficient r = -.6

2. In a class of 30, 10 wear glasses, 20 are right-handed, and 5 are left-handed and wear glasses. If a student is randomly selected, determine the probability that: a) the student doesn’t wear glasses b) the student is left-handed and doesn’t wear glasses c) the student is left-handed or doesn’t wear glasses. d) Given that the student wears glasses, what is the probability that the student is right- handed?

3. Three coins are tossed. The probability of no heads occurring is .125, the probability of 1 head is .375, the probability of 2 heads is .375, and the probability 3 heads is .125. If an odd number of heads appear, you receive $100. If two heads appear, you receive $75. If no heads appear, you pay $65. Let X denote the dollar amount one wins from playing the game once. a) What is the expected value of the game, E(X)? b) What is the probability of winning at least $75?

4. A report states that 90% of all U.S. citizens have a driver’s license. a) In a sample of 25 randomly selected U. S. citizens, what is the probability that at most 23 of them have their driver’s licenses? b) In the same sample of 25, what is the probability that between 20 and 25, inclusive, have their driver’s licenses? c) In a sample of 500, what is the approximate probability that at least 460 have their driver’s licenses?

5. A sample of 55 animals of a common breed are injected with adrenaline and their blood sugar levels are recorded. The mean and standard deviation are found to be 126.9 mg/ml and 10.5 mg/ml, respectively. a) Give a point estimate of the population mean b) Find a 95% error margin. c) Determine a 95% confidence interval for the population mean. d) What sample size is needed for a 95% error margin to be 1.3? 6. From a sample of 2300 insurance policies, 391 had at least one claim made. a) Determine the 99% confidence interval for the population proportion of insurance policies with at least one claim. b) What is the conclusion for testing the null hypothesis that the probability of at least one claim is .16 versus the alternative that the probability of at least one claim is different from .16 at the   .05 level?

7. Data are collected from 45 popular fast-food restaurants to determine how many calories are in 3 ounces of french fries. The sample mean is found to be 250 calories, and the sample standard deviation is 21.73. At  = 0.01, test the claim that the mean number of calories in 3 ounces of french fries is greater than 244. Show all the steps as you work through the hypothesis test by formulating the hypotheses, giving the rejection region, calculating the test statistic, and stating the conclusion.

8. The sepal width on iris flowers of two varieties, iris setosa and iris versicolor are: Setosa 23 29 32 34 30 36 40 42 44 32 34 32 36 32 34 Versicolo 22 23 22 20 24 23 24 25 28 30 19 19 r The following summary statistics were found. setosa versicolo r Mean 34 23.25 Standard Deviation 5.25 3.33 a) Draw two stem-leaf diagrams, one for each variety. b) From the diagrams, make a comparison of the two distributions; include the mean and the median in your comparison. c) Construct a 90% confidence interval for the difference in mean sepal widths. d) State any assumptions you used to determine the confidence interval in (c).

9. Mileage tests are conducted to compare a new versus a conventional spark plug. A sample of 6 cars is included in the study. Mileage is recorded for each car using the new and conventional plug with the following results. Car 1 2 3 4 5 6 New 26.4 10.3 15.8 16.5 32.5 8.3 Conventional 24.3 9.8 16.9 17.2 30.5 7.9 Construct a 95% confidence interval for the difference in mean spark plug mileages.

10. Census data reports 26% of U.S. households consist of a married couple with children, 29% consist of a married couple with no children, 9% are households consisting of a single parent with children, and 36% consist of a one person or other (e.g. roommates, siblings, etc.). A sample of 411 households from Laurel, Maryland, is shown in the table. Use a 5% level of significance to test the claim that the distribution of households in Laurel fits the census distribution. Show all the steps as you work through the hypothesis test by formulating the hypotheses, giving the rejection region, calculating the test statistic, and stating the conclusion. Married & children Married & no children Single parent One person or other 125 132 33 121