Problem
Question 23 Score on last try: 0.3 of 1 pts. See Details for more. \( > \) Next question \( \rightleftarrows \) Get a similar question You can retry this question bel Testing Claims You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \). \[ \begin{array}{l} H_{o}: p=0.8 \\ H_{a}: p<0.8 \end{array} \] You obtain a sample of size \( n=186 \) in which there are 142 successful observations. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic \( = \) What is the \( \mathrm{p} \)-value for this sample? (Report answer accurate to three decimal places.) \( \mathrm{p} \)-value \( = \) The \( p \)-value is... less than (or equal to) \( \alpha \)
Solution
Step 1 ：Calculate the sample proportion: \(\hat{p} = \frac{142}{186}\)
Step 2 ：Compute the test statistic: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\)
Step 3 ：Find the p-value using a standard normal distribution table or calculator
