19.9: Randomly selected records of 140 convicted criminals reveal that their crimes were committed on
19.9: Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week:
| Category | Observed |
| Mon | 17 |
| Tue | 21 |
| Wed | 22 |
| Thu | 18 |
| Fri | 23 |
| Sat | 24 |
| Sun | 15 |
- 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.
- Specify the approximate \(p\) -value for this test result.
- 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.
- Test the null hypothesis that this coin is unbiased, that is, that heads and tails are equally likely to appear in the long run.
- Specify the approximate \(p\) -value for this test result.
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:
- Using the $.05$ level of significance, test the null hypothesis for gender and attitude toward gun control.
- Specify the approximate \(p\) -value for the test result.
- How might these results be reported in the literature?
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 subsequent five-year period, these same drivers were cited for the following number of moving violations:
- Why might the Mann-Whitney U test be preferred to the t test for these data?
- Use U to test the null hypothesis at the .05 level of signi fi cance.
- Specify the approximate p -value for this test result.
20.6 A social psychologist wishes to test the assertion that our attitude toward other people tends to re fl ect 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.)
- Use \(T\) to test the null hypothesis at the .01 level.
- Specify the approximate \(p\) -value for this test result.
20.7 Does background music infl uence 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 a re as follows (higher scores refl ect better comprehension):
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