Problem

A publisher reports that 38 \% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually above the reported percentage. A random sample of 350 found that $42 \%$ of the readers owned a particular make of car. Is there sufficient evidence at the 0.10 level to support the exccutive's claim? Step 2 of 7: Find the value of the test statistic. Round your answer to two decimal places. Answer Tables Keypad

Solution

Step 1 :The problem is asking for the value of the test statistic in a hypothesis test for a proportion. The test statistic in this case is a z-score, which is calculated as \( (p̂ - p0) / \sqrt{(p0 * (1 - p0)) / n} \), where \( p̂ \) is the sample proportion, \( p0 \) is the population proportion under the null hypothesis, and \( n \) is the sample size. In this case, \( p̂ = 0.42 \), \( p0 = 0.38 \), and \( n = 350 \).

Step 2 :Substitute the given values into the formula: \( z = (0.42 - 0.38) / \sqrt{(0.38 * (1 - 0.38)) / 350} \)

Step 3 :Calculate the z-score to get the test statistic for the hypothesis test.

Step 4 :The calculated z-score is 1.54.

Step 5 :Final Answer: The value of the test statistic is \( \boxed{1.54} \).

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Source: https://solvelyapp.com/problems/sI6JOxDdAx/

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