Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of college students who own cars is less than $35 \%$. Identify the type I error. Choose the correct answer below. A. Reject the null hypothesis that the percentage of college students who own cars is equal to $35 \%$ when that percentage is actually equal to $35 \%$. B. Reject the null hypothesis that the percentage of college students who own cars is less than $35 \%$ when that percentage is actually less than $35 \%$. c. Fail to reject the null hypothesis that the percentage of college students who own cars is less than $35 \%$ when the percentage is actually equal to $35 \%$. D. Fail to reject the null hypothesis that the percentage of college students who own cars is equal to $35 \%$ when that percentage is actually less than $35 \%$.
Solution
Step 1 ：Identify the type I error and the type II error that correspond to the given hypothesis: The percentage of college students who own cars is less than $35 \%$.
Step 2 ：In hypothesis testing, a type I error occurs when the null hypothesis is true, but is rejected. It is asserting something that is absent, a false hit. A type II error occurs when the null hypothesis is false, but erroneously fails to be rejected. It is failing to assert what is present, a miss.
Step 3 ：In this case, the null hypothesis is that the percentage of college students who own cars is less than or equal to $35 \%$. The alternative hypothesis is that the percentage of college students who own cars is more than $35 \%$.
Step 4 ：A type I error would be to reject the null hypothesis when it is true i.e., to conclude that the percentage of college students who own cars is more than $35 \%$ when it is actually less than or equal to $35 \%$.
Step 5 ：Therefore, the correct answer is A. Reject the null hypothesis that the percentage of college students who own cars is equal to $35 \%$ when that percentage is actually equal to $35 \%$.
Step 6 ：Final Answer: \(\boxed{\text{A. Reject the null hypothesis that the percentage of college students who own cars is equal to } 35 \% \text{ when that percentage is actually equal to } 35 \%}\)
