# approximate p -value

Complete the following exercises located at the end of each chapter and put them into a Word document to be submitted as directed by the instructor.

Show all relevant work; use the equation editor in Microsoft Word when necessary.

Chapter 19, numbers 19.9, 19.10, 19.13, 19.14, and 19.16

Chapter 20, numbers 20.5, 20.6, 20.7, and 20.10

19.9 Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week:

(a) Using the .01 level of signiﬁcance, test the null hypothesis that in the underlying population, crimes are equally likely to be committed on any day of the week.

(b) Specify the approximate p -value for this test result.

(c) How might this result be reported in the literature?

19.10 While playing a coin-tossing game in which you are to guess whether heads or tails will appear, you observe 30 heads in a string of 50 coin tosses.

(a) Test the null hypothesis that this coin is unbiased, that is, that heads and tails are equally likely to appear in the long run.

(b) Specify the approximate p -value for this test result.

*19.13 In 1912, over 800 passengers perished after the ocean liner Titanic collided with an iceberg and sank. The table below compares the survival frequencies of cabin and steerage passengers.

(a) Using the .05 level of signiﬁcance, test the null hypothesis that survival rates are independent of the passengers’ accommodations (cabin or steerage).

(b) Assuming a signiﬁcant c2 ,estimate the strength of the relationship.

(c) To more fully appreciate the importance of this relationship, calculate an odds ratio to determine how much more likely a cabin passenger is to have survived than a steerage passenger.

19.14 In a classic study, Milgram et al . “lost” stamped envelopes with ﬁctitious addresses (Medical Research Association, Personal Address, Friends of Communist Party, and Friends of Nazi Party).* One hundred letters with each address were distributed among four locations (shops, cars, streets, and phone booths) in New Haven Connecticut, with the following results:

CHI-SQUARE (b2) TEST FOR QUALITATIVE DATA

(a) Using the .05 level of signiﬁcance, test the null hypothesis that address does not matter in the underlying population.

(b) Specify the approximate p -value for this result.

(c) Assuming c2 is signiﬁcant, estimate the strength of this relationship.

(d) How might these results be reported in the literature?

(e) Collapse the original 4 x 2 table to a 2 x 2 table by combining the results for the two neutral addresses and for the two inﬂammatory addresses. Calculate the odds ratio for returned letters.

19.16 A social scientist cross-classiﬁes the responses of 100 randomly selected people on the basis of gender and whether or not they favor strong gun control laws to obtain the following:

(a) Using the .05 level of signiﬁcance, test the null hypothesis for gender and attitude toward gun control.

(b) Specify the approximate p -value for the test result.

(c) How might these results be reported in the literature?

Chapter 20, numbers 20.5, 20.6, 20.7, and 20.10

20.5 A group of high-risk automobile drivers (with three moving violations in one year) are required, according to random assignment, either to attend a trafﬁc school or to perform supervised volunteer work. During the sub-sequent ﬁve-year period, these same drivers were cited for the following number of moving violations:

20.6 A social psychologist wishes to test the assertion that our attitude toward other people tends to reﬂect our perception of their attitude toward us. A randomly selected member of each of 12 couples who live together is told (in private) that his or her partner has rated that person at the high end of a 0 to 100 scale of trustworthiness. The other member is told (also in private) that his or her partner has rated that person at the low end of the trustworthiness scale. Each person is then asked to estimate, in turn, the trustworthiness of his or her partner, yielding the following results. (According to the original assertion, the people in the trustworthy condition should give higher ratings than should their partners in the untrustworthy condition.)

(a) Use T to test the null hypothesis at the .01 level.

(b) Specify the approximate p -value for this test result.

20.7 Does background music inﬂuence the scores of college students on a reading comprehension test? Sets of 10 randomly selected students take a reading comprehension test with rock, country, or classical music in the background. The results are as follows (higher scores reﬂect better comprehension):

(a) Why might the H test be preferred to the F test for these data?

(b) Use H to test the null hypothesis at the .05 level of signiﬁcance.

20.10 Use H rather than F to test the weight change data recorded in Review Question 16.13 on page 381.

16.13 Twenty-three overweight male volunteers are randomly assigned to three different treatment programs designed to produce a weight loss by focusing on either diet, exercise, or the modiﬁcation of eating behavior. Weight changes were recorded, to the nearest pound, for all participants who completed the two-month experiment. Positive scores signify a weight drop; negative scores, a weight gain.