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: \square \\) select \\( h_1: \square \\) select this hypothesis test is a select test.

Explanation:

• Null Hypothesis (\(H_0\)): The null hypothesis is a statement of no difference. In this case, we assume that the mean amount spent by college students (\(\mu_1\)) is equal to the mean amount spent by non - college students (\(\mu_2\)) for a used car. So \(H_0:\mu_1=\mu_2\).
• Alternative Hypothesis (\(H_1\)): The researcher's claim is that college students spent less for a used car than those in the general population. So we are testing if \(\mu_1\) (college students' mean) is less than \(\mu_2\) (non - college students' mean), which gives us \(H_1:\mu_1 < \mu_2\).
• Type of Test: Since the alternative hypothesis has a less - than (\(<\)) sign, this is a left - tailed hypothesis test.

Answer:

\( H_0: \mu_1 = \mu_2 \) (where \(\mu_2\) is the mean for non - college students), \( H_1: \mu_1 < \mu_2 \)
This hypothesis test is a left - tailed test.