Question 13
of 14 Step 6 of 7
$01: 01: 52$
A publisher reports that $27 \%$ of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually over the reported percentage. A random sample of 400 found that $32 \%$ of the readers owned a particular make of car. Is there sufficient evidence at the 0.02 level to support the executive's claim?

Step 6 of 7: Make the decision to reject or fail to reject the null hypothesis.
Answer 2 Points
Reject Null Hypothesis

Answer

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Answer

$ \boxed{\text{Reject Null Hypothesis}} $

Steps

Step 1 ：Calculate the standard error using the formula $ \text{SE} = \sqrt{\frac{p_0(1-p_0)}{n}} $ where $ p_0 = 0.27 $ and $ n = 400 $

Step 2 ：Calculate the test statistic using the formula $ z = \frac{\hat{p} - p_0}{\text{SE}} $ where $ \hat{p} = 0.32 $

Step 3 ：Find the critical value for a one-tailed test at the 0.02 significance level using the normal distribution

Step 4 ：Compare the test statistic to the critical value

Step 5 ：If the test statistic is greater than the critical value, reject the null hypothesis

Step 6 ：$ \boxed{\text{Reject Null Hypothesis}} $