Problem

\[ \begin{array}{l} H_{0}: p=0.72 \\ H_{1}: p>0.72 \end{array} \] Your sample consists of 130 subjects, with 91 successes. Calculate the test statistic, rounded to 2 decimal places \[ z= \]

Solution

Step 1 :Define the null hypothesis \(H_{0}: p=0.72\) and the alternative hypothesis \(H_{1}: p>0.72\).

Step 2 :The sample consists of 130 subjects, with 91 successes.

Step 3 :Calculate the sample proportion \(\hat{p}\) by dividing the number of successes by the sample size: \(\hat{p} = \frac{91}{130}\).

Step 4 :Substitute \(\hat{p} = 0.7\), \(p_0 = 0.72\), and \(n = 130\) into the formula for the test statistic: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}\).

Step 5 :Calculate the test statistic to get \(z = -0.51\).

Step 6 :Final Answer: \(\boxed{-0.51}\)

From Solvely APP
Source: https://solvelyapp.com/problems/28101/

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