Problem

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 $35 \%$.

Answer

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Answer

Final Answer: \(\boxed{\text{A. Reject the null hypothesis that the percentage of college students who own cars is equal to } 35 \% \text{ when that percentage is actually equal to } 35 \%}\)

Steps

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: \(\boxed{\text{A. Reject the null hypothesis that the percentage of college students who own cars is equal to } 35 \% \text{ when that percentage is actually equal to } 35 \%}\)

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