Psyc 21621: Quantitative Methods I

Practice Exam Mike Moore

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HELPFUL FORMULAS:

Median Location = (N +1)/2

Mean = X/N

Hinge Location = (Median location +1)/2

Z = (X – X )/s OR ( X -μ)/σ

Variance = [(X - X )2]/(N -1)

Standard deviation = √(s2) Section I: Multiple Choice* (Each question is worth 1 point) *See answers last page

1. If you want to study the effect of hormonal changes as boys reach adolescence, your sample would most likely include a. pre-adolescent and post-adolescent boys b. adolescent boys c. pre-adolescent and post-adolescent girls d. adult men

2. Which of the following is the appropriate pairing? a. Population:Statistic; Sample:Parameter b. Population:Parameter; Sample:Statistic c. Population:Statistic: Statistic:Parameter d. Parameter:Statistic; Sample:Population

3. When given a cup of coffee before a race, a sample of runners were found to run the race faster. If we then conclude that on average runners run faster after drinking coffee, this would be an example of a. an illogical inference b. an inferential inference c. a statistical inference d. a descriptive inference

4. In order for a researcher to be able to estimate the parameters of a population from his or her sample, the sample must be a. very large b. racially diverse c. low in variability d. random

5. Which of the following is a logical, as opposed to a statistical, conclusion? a. If a sample of mice overdoses on morphine in novel contexts, the population of micewill also overdose b. If mice overdose on morphine in novel contexts, human beings may also overdose in novel contexts c. If a relationship is present, there is also a difference d. If one child is left-handed, then all children are left-handed

6. The major difference between an interval and a ratio scale is that a. with an interval scale you know which values represent more of the quantity b. with an interval scale you can speak meaningfully about a score of 0 c. with a ratio scale you can speak meaningfully about a score of 0 d. both scales carry the same level of information

7. When we speak of paw-lick latency as a measure of temperature sensitivity, latency is a. an independent variable b. a categorical variable c. a continuous variable d. a discrete variable 8. If we want to obtain a random sample of people to interview, we could best do so by a. drawing random numbers from a table and linking a number to a person b. take every 10th name out of the telephone book c. knock on doors and interview whoever answers d. ask for volunteers

9. For the following equation, which mathematical operation should be performed first? 6  2[7 *(4 1)] 3 1 a. 3 – 1 b. 6 + 2 c. 4 + 1 d. 2 x 4

10. For the set of numbers 1, 17, 19, 30, 87, X5 refers to a. 1, 17, 19, 30 b. 1, 17, 19, 30, 87 c. 87 d. 5

11. The “real lower limit” of an interval in a histogram is a. the lowest integer value for scores in that interval b. the midpoint of the interval c. the lowest continuous value that would be rounded up into that interval d. the smallest width of the interval

12. “5s” represents what numbers on a stem-and-leaf display according to Tukey? a. 50 – 51 b. 52 – 53 c. 54 – 55 d. 56 – 57

13. In making plots of data, which of the following rules is true? a. Three-dimensional plots should never be used b. Rules of graphical presentation are prescriptive and should never be broken c. The ultimate goal in making plots is to make data attractive d. The point of representing data graphically is better communication

14. In deciding on the number of stems to use in a stem-and-leaf display, a. you should always break the stems into 5 stems per every 10 units b. you should normally make all of the stems the same width c. you should generally use 10 stems in all d. you should disregard the frequencies of the data

15. A negatively skewed distribution a. has a tail pointing to the left b. has a tail pointing to the right c. is symmetric d. is also positively skewed

16. The median has at least one advantage over the mean in that a. it is not much affected by extreme scores b. it is easier to calculate than the mode c. it is usually closer to the population mean than the mode d. it varies less from sample to sample 17. Which of the following is useful with data collected with nominal scales? a. median b. mode c. mean d. none of the above

18. The measure of central tendency that is most useful is estimating population characteristics because it is less variable from sample to sample is the a. mode b. median c. mean d. All of the above are equally useful in estimating characteristics of the population

19. For the data set [1, 3, 3, 5, 5, 5, 7, 7, 9], the value “5” represents a. the mode b. the median c. the mean d. all of the above

20. Which of the following is defined algebraically? a. mean b. median c. median location d. both (a) and (c)

21. The population variance is a. an estimate of the sample variance b. calculated exactly like the sample variance c. a biased estimate d. usually an unknown that we try to estimate

22. The variance can best be thought of as the a. average of the squared deviations from the mean b. average of the absolute deviations from the mean c. average of the squared deviations from the median d. the square of the mean

23. What do we mean by an unbiased statistic? a. A statistic that equals the sample mean b. A statistic whose average is very stable from sample to sample c. A statistic used to measure racial diversity d. A statistic whose long range average is equal to the parameter it estimates

24. In a boxplot the width of the box encompasses a. all of the observed values b. all but the most extreme values c. approximately 50% of the observed values d. the center-most 10% of the values

25. If we know that a set of test scores has a mean of 75 and a standard deviation of 8, we would conclude that a. the average deviation from the mean is about 8 points b. the average person will have a score of 75 + 8 = 83 c. more people are above 75 than below it d. you can’t tell anything about how scores lie relative to the mean 26. If behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know a. the mean b. the standard deviation c. the sample size d. both (a) and (b), but not (c)

27. Knowing that the data are normally distributed allows me to a. calculate the probability of obtaining a score greater than some specified value b. calculate the probability of obtaining a score of exactly 1 c. calculate what range of values are unlikely to occur by chance d. (a) and (c), but not (b)

28. If we know that the probability for z > 1.5 is .067, then we can say that a. the probability of exceeding the mean by more than 1.5 standard deviations is .067 b. the probability of being more than 1.5 standard deviations away from the mean is .134 c. 86.6% of the scores are less than 1.5 standard deviations from the mean d. all of the above

29. If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately a. 30 – 70 b. 35 – 50 c. 45 – 55 d. 70 – 90

30. Which of the following is not always true of a normal distribution? a. It is symmetric b. It has a mean of 0 c. It is unimodal d. All of the above are always true Section II: Problems* (Each question is worth 5 points) *Remember to show all (if any) work, partial credit will be given

31. Create a histogram for these data using an interval of 5 (e.g., 0 to 5, 6 to 10). 1 9 15 20 25 29 32 40 47 2 10 16 21 26 30 35 42 49 3 11 16 22 27 30 35 42 50 5 13 18 24 28 31 35 43 50 6 14 19 24 28 31 37 45 51 7 14 20 25 29 32 39 46 59

32. Given the following data set, demonstrate that multiplying the mean by a constant of 2 is equivalent to multiplying each value by that constant (2) and then calculating the mean. 1 2 3 4 33. Answer the following questions based on this set of numbers:

1 2 2 3 3 3 4 5

a. What is the range? b. What is the variance? c. What is the standard deviation?

34. The birth weight of healthy, full term infants in the United States in nearly normally distributed. The mean weight is 3,500 grams, and the standard deviation is 500 grams. a. What percent of healthy newborns will weigh more than 3,250 grams (use z-table E.10 beginning on page 527in your text)? b. What weights would 95% of all healthy newborns tend to fall between? c. What is the z-score for an infant who weighs 2,750 grams? Practice Exam Answer Key

1. A 32. The mean, multiplied by 2 = 2. B 1 2  3  4  10   * 2    * 2  2.5* 2  5 3. C  4   4  4. D The values, multiplied by two 5. B are: 2, 4, 6, 8. 6. C The mean of these values = 7. C 2  4  6  8 8. A  5 9. C 4 10. C The two are clearly equivalent. 11. C 33. 12. D a. range = 4 13. D b. variance = 1.55 14. B c. standard deviation = 1.25 15. A 16. A 34. 17. B a. 69% 18. C b. 95% would fall between 19. D 2,520 grams and 4,480 20. D grams 21. D c. z = -1.5 22. A 23. D 24. C 25. A 26. D 27. D 28. D 29. A 30. B 31.

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