Problem
For students who first enrolled in two-year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was 0.397 . The president of a certain junior college believes that the proportion of students who enroll in her institution have a higher completion rate. (a) State the null and alternative hypotheses in words. (b) State the null and alternative hypotheses symbolically. (c) Explain what it would mean to make a Type I error. (d) Explain what it would mean to make a Type II error. B. Among students wno rirst enroll in two-year pubil institutions, the compietion rate is U.syi. C. Among students who enroll at the certain junior college, the completion rate is 0.397 . D. Among students who enroll at the certain junior college, the completion rate is greater than 0.397 . State the alternative hypothesis in words. Choose the correct answer below. A. Among students who enroll at the certain junior college, the completion rate is 0.397 . B. Among students who enroll at the certain junior college, the completion rate is less than 0.397 . C. Among students who enroll at the certain junior college, the completion rate is greater than 0.397 . D. Among students who first enroll in two-year public institutions, the completion rate is 0.397 . (b) State the hypotheses symbolically. \begin{tabular}{l|l|l|} $\mathrm{H}_{0}:$ & $\nabla$ & $\nabla$ \\ $\mathrm{H}_{1}:$ & $\nabla$ & $\square$ \\ \hline$\nabla$ \end{tabular} (Type integers or decimals. Do not round.)
Solution
Step 1 ：The alternative hypothesis in words is 'Among students who enroll at the certain junior college, the completion rate is greater than 0.397'.
Step 2 ：Symbolically, this is represented as H1: p > 0.397.
