Problem
A publisher reports that $43 \%$ of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually under the reported percentage. A random sample of 100 found that $35 \%$ of the readers owned a particular make of car. Is there sufficient evidence at the 0.05 level to support the executive's claim? Step 7 of 7: State the conclusion of the hypothesis test. Answer Tables Keypad Keyboard Shortcuts
Solution
Step 1 ：State the null hypothesis: \( H_0: p = 0.43 \)
Step 2 ：State the alternative hypothesis: \( H_1: p < 0.43 \)
Step 3 ：Calculate the standard error: \( SE = \sqrt{ \frac{p(1-p)}{n} } \)
Step 4 ：Calculate the z-score: \( z = \frac{\hat{p} - p}{SE} \)
Step 5 ：Find the p-value corresponding to the z-score
Step 6 ：Compare the p-value to the significance level \( \alpha = 0.05 \)
Step 7 ：\(\boxed{\text{There is not enough evidence to support the executive's claim at the 0.05 level.}}\)
