91Ó°ÊÓ

The examinations in a large multisection statistics class are scaled after grading so that the mean score is 75 . The professor thinks that students in the 8:00 A.M. class have trouble paying attention because they are sleepy and suspects that these students have a lower mean score than the class as a whole. The students in the 8:00 A.M. class this semester can be considered a sample from the population of all students in the course, so the professor compares their mean score with 75 . State the hypotheses \(H_{0}\) and \(H_{a}\).

The average income of American women who work fulltime and have only a high school degree is \(\$ 35,713\). You wonder whether the mean income of female graduates from your local high school who work full-time but have only a high school degree is different from the national average. You obtain income information from an SRS of 62 female graduates who work fulltime and have only a high school degree and find that \(x^{-} \bar{x}=\$ 35,053\). What are your null and alternative hypotheses?

A test of \(H_{0}: \mu=0\) against \(H_{a}: \mu \neq 0\) has test statistic \(z=1.65\). Is this test statistically significant at the \(5 \%\) level \((\alpha=0.05)\) ? Is it statistically significant at the \(1 \%\) level \((\alpha=0.01)\) ?