91Ó°ÊÓ

Exercises 5.50 to 5.55 include a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Find the value of the standardized \(z\) -test statistic in each situation. Test \(H_{0}: p=0.25\) vs \(H_{a}: p<0.25\) when the sample has \(n=800\) and \(\hat{p}=0.235,\) with \(S E=0.018\).

In Exercises 5.56 and \(5.57,\) find the p-value based on a standard normal distribution for each of the following standardized test statistics. (a) \(z=0.84\) for an upper tail test for a difference in two proportions (b) \(z=-2.38\) for a lower tail test for a difference in two means (c) \(z=2.25\) for a two-tailed test for a correlation

Hearing Loss in Teenagers A recent study" found that, of the 1771 participants aged 12 to 19 in the National Health and Nutrition Examination Survey, \(19.5 \%\) had some hearing loss (defined as a loss of 15 decibels in at least one ear). This is a dramatic increase from a decade ago. The sample size is large enough to use the normal distribution, and a bootstrap distribution shows that the standard error for the proportion is \(S E=0.009 .\) Find and interpret a \(90 \%\) confidence interval for the proportion of teenagers with some hearing loss.

Exercise and Gender The dataset ExerciseHours contains information on the amount of exercise (hours per week) for a sample of statistics students. The mean amount of exercise was 9.4 hours for the 30 female students in the sample and 12.4 hours for the 20 male students. A randomization distribution of differences in means based on these data, under a null hypothesis of no difference in mean exercise time between females and males, is centered near zero and reasonably normally distributed. The standard error for the difference in means, as estimated from the standard deviation of the randomization differences, is \(S E=2.38 .\) Use this information to test, at a \(5 \%\) level, whether the data show that the mean exercise time for female statistics students is less than the mean exercise time of male statistics students.