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Chapter 8: Problem 98

Refer to Exercise \(8.97 .\) Suppose 14 out of 20 voters in Pennsylvania report having voted for an independent candidate. The null hypothesis is that the population proportion is \(0.50 .\) What value of the test statistic should you report?

Short Answer

Expert verified
The test statistic to be reported is 2.

Step by step solution

01

Understanding the Problem

The null hypothesis \(H_0\) states that the population proportion \(p\) is 0.50. We have a sample of 20 voters where 14 have voted for an independent candidate. Let's denote the number of successes (votes for an independent candidate) as \(X = 14\) and the sample size as \(n = 20\).
02

Calculate the Sample Proportion

We can calculate the sample proportion \(\hat{p}\) using the formula \(\hat{p} = X/n\). Substituting the given values, \(\hat{p} = 14/20 = 0.70\).
03

Calculate the Test Statistic

The test statistic \(z\) for testing a proportion is calculated as \(z = (\hat{p} - p_0) / \sqrt{(p_0(1-p_0))/n}\), where \(p_0\) is the null hypothesis proportion. Substituting the values, \(z = (0.70 - 0.50) / \sqrt{(0.50(1-0.50))/20} = 2\).

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