1. (a) 0, 1 (b) 0.95 (c) 0.05
2. (a) 0.63 (b) 0.82 (c) 0.28. We cannot estimate it directly from the table because the study is a case-control study and the number of cases and controls are arbitrarily decided by the investigators.
3. No. First, the measure from previous days affect the measurement of the following days, so the seven trials are not independent. Second, due to the difference of traffic during the weekdays and the weekend, the probability is not constant over the seven days.
4. (a) 0.474 (b) mean=2.5, variance=1.875
5. (a) 0.13 (b) 85.2 mm Hg
6. (a) smaller (b) The probability of obtaining a sample at least as extreme as the observed sample assuming the null hypothesis is true (c) greater than 0.05 (d) Use z-test when population variance (¥ò2) is known. Use t-test when population variance is unknown. Both tests require large sample size or underlying distribution to be normal. (e) increases
7. (3.96, 5.02) liters. Assumptions: The distribution of FVC in the population (all individuals with history of exercise-induced asthma) is normal. Individuals are independent.
8. H0: muI= muII (The mean degrees of violent behavior in group I and group II are the same. OR There is no association between TV violence exposure during childhood and the degrees of violent behavior.) HA: muI ¡Á muII. t=2.14 (d.f.=35); Since t=2.11 is larger than the critical value 2.0301, p-value is less than 0.05.
We reject the null hypothesis and conclude that there is statistically significant evidence of association between childhood TV violence exposure and the degrees of violent behavior.
9. H0: mu1= mu2 (The mean reductions of cholesterol levels caused by the new drug and the old drug are the same in elderly people.)
HA: mu1 and mu2 are different.
T=2.3451, p-value =0.031
We reject the null hypothesis and conclude that the cholesterol reductions caused by two treatments are significantly different. The assumptions are that underlying population cholesterol reductions are normally distributed and that their variances are equal (from the degrees of freedom and the title ¡°Student¡¯s t-test¡±).
10.(a) P(Reject H0 | H0 is true) = P(Declare inadequacy | Adequate ) = 0.07
(b) Power = P(Reject H0 | vaccination rate 70%) =1-0.67 = 0.33
(c) Set the null hypothesis as the conservative status quo: i.e. ¡°The vaccination rate in the community is less than 80%¡± or ¡°The vaccination rate is inadequate.¡±) and/or increase the sample size to control for type II error (or power) as well as type I error.
11. The researcher has all necessary information (null hypothesis, type 1 error, sample size) except 1) the population variance of the cholesterol level among the youths in Bronx and 2) the ¡®reasonably conservative value (or the target effect size)¡¯ of the cholesterol level among Bronx youths who have HIV.
12. 96 people