Question

decide whether the normal sampling distribution can be used. if it can be used, test the claim about the population proportion ( p ) at the given level of significance ( alpha ) using the given sample statistics. claim: ( p
eq 0.24 ); ( alpha = 0.01 ); sample statistics: ( hat{p} = 0.17 ), ( n = 200 ) ( h_{a}: p < 0.24 ) c. ( h_{0}: p leq 0.24 ) ( h_{a}: p > 0.24 ) d. the test cannot be performed. determine the critical value(s). select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the critical value(s) is/are - 2.58, 2.58 (round to two decimal places as needed. use a comma to separate answers as needed.) b. the test cannot be performed. find the z - test statistic. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. ( z = ) (round to two decimal places as needed) b. the test cannot be performed.

Explanation:

Step1: Check if normal sampling distribution can be used

We need to check \(np\geq5\) and \(n(1 - p)\geq5\). Given \(p = 0.24\), \(n=200\).
\(np=200\times0.24 = 48\geq5\)
\(n(1 - p)=200\times(1 - 0.24)=200\times0.76 = 152\geq5\)
So, normal sampling distribution can be used.

Step2: Calculate the z - test statistic

The formula for the z - test statistic in a proportion test is \(z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}\)
Here, \(\hat{p}=0.17\), \(p = 0.24\), \(n = 200\)

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Answer:

A. \(z=-2.32\)