For a random sample of 25 students, 20 passed the exam and 5 did not pass the exam. Test the following hypotheses at the .01 level of significance:

$\begin{array}{l}
H_{0}: \pi=75 \
H_{1}: \pi \neq .75
\end{array}$

Question

For a random sample of 25 students, 20 passed the exam and 5 did not pass the exam. Test the following hypotheses at the .01 level of significance:

$\begin{array}{l}
H_{0}: \pi=75 \
H_{1}: \pi \neq .75
\end{array}$

Quizplus · Accepted Answer

The Answer is

z=\frac{p-\pi_{0}}{\sqrt{\frac{\pi_{0}\left(1-\pi_{0}\right)}{n}}}=\frac{.80-.75}{\sqrt{\frac{75(1-.75)}{25}}}=\frac{.05}{\sqrt{\frac{75(.25)}{25}}}=\frac{.05}{.0866}=.577

Using the z table, we find critical values of +/-2.57 (split alpha in ½ given a two-tailed test thus 1 - .005 or .995; find P(z) = .995 in the table; this corresponds to z of 2.57). Since z of .577 (test statistic value) is less than our critical value (+2.57), we fail to reject the null hypothesis.

For a Random Sample of 25 Students, 20 Passed the Exam