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