Problem
> Next question \( \rightleftarrows \) Get a similar question You can retry this questio Hypothesis Test for a Population Proportion You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.05 \). \[ \begin{array}{l} H_{o}: p=0.86 \\ H_{a}: p>0.86 \end{array} \] You obtain a sample of size \( n=257 \) in which there are 233 successful observation What is the test statistic for this sample? (Report answer accurate to three decima test statistic \( = \) What is the \( p \)-value for this sample? (Report answer accurate to three decimal place \( p \)-value \( = \) The \( \mathrm{p} \)-value is... less than (or equal to) \( \alpha \) greater than \( \alpha \) \( 6^{6} \) This test statistic leads to a decision to... O Type here to search
Solution
Step 1 ：\( Z = \frac{(\frac{233}{257}) - 0.86}{\sqrt{\frac{0.86(1-0.86)}{257}}} \)
Step 2 ：\( Z \approx 2.921 \)
Step 3 ：\( p \)-value \( \approx 0.002 \)
