Question

prices of a used car for a specific year the kelley blue book stated that the average price of a used car was $15,900. a researcher wanted to see if the mean amount of money spent by college students for a used car was less than the mean amount of money spent for a used car in general. she randomly selected 50 college students who purchased a used car for college and found that the sample had a mean of $15,333. for the general population who were not attending college at that time, the mean amount of money spent by 50 non - college students for a used car was $15,427 and the population standard deviation was $289. at \\( \alpha = 0.05 \\), can it be concluded that college students spent less for a used car than those in the general population? use \\( \mu_1 \\) for the mean amount spent by college students. use the critical value method and table. part: 0 / 5 part 1 of 5 (a) state the hypotheses and identify the claim. \\( h_0:\\) \\( h_1:\\) this hypothesis test is a test.

Explanation:

• Null Hypothesis (\(H_0\)): In hypothesis testing, the null hypothesis typically assumes no difference or equality. Here, we assume that the mean amount spent by college students (\(\mu_1\)) is equal to the mean amount spent by the general population (\(\mu_2\)), so \(H_0: \mu_1=\mu_2\).
• Alternative Hypothesis (\(H_1\)): The researcher wants to test if college students spent less. So we set the alternative hypothesis as \(H_1: \mu_1 < \mu_2\), which represents the claim.
• Type of Test: Since the alternative hypothesis has a less - than (\(<\)) sign, this is a left - tailed hypothesis test.

Answer:

\(H_0: \mu_1 = \mu_2\)
\(H_1: \mu_1 < \mu_2\)
This hypothesis test is a left - tailed test. (The claim is that college students spent less for a used car than those in the general population, which corresponds to \(H_1\).)