Answer to Question #347438 in Statistics and Probability for CHEN

Question

A school principal claims that more than 67% of the 700 students of their school prefer printed modules. Test the hypothesis using 95% level of confidence.

Answer 1

$H_0:p\le0.67$

$H_a:p>0.67$

This corresponds to a right-tailed test, for which a z-test for one population proportion will be used.

Evidence:

Based on the information provided, the significance level is $\alpha = 0.05 ,$ and the critical value for a right-tailed test is $z_c = 1.6449.$

The rejection region for this right-tailed test is $R = \{z: z >1.6449\}.$

The z-statistic is computed as follows:

$$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{X/700-0.67}{\sqrt{\dfrac{0.67(1-0.67)}{700}}}$$