Question

a professor believes that for the introductory art history classes at his university, the mean test score of students in the evening classes is lower than the mean test score of students in the morning classes. he collects data from a random sample of 200 students in evening classes and finds that they have a mean test score of 87.8. he knows the population standard deviation for the evening classes to be 6.7 points. a random sample of 250 students from morning classes results in a mean test score of 88.6. he knows the population standard deviation for the morning classes to be 1.8 points. test his claim with a 98% level of confidence. let students in the evening classes be population 1 and let students in the morning classes be population 2. step 1 of 3: state the null and alternative hypotheses for the test. fill in the blank below. $h_0:mu_1=mu_2$ $h_a:mu_1$ ____ $mu_2$ answer > < $
eq$

Explanation:

Step1: Identify the claim

The professor claims that the mean test - score of students in the evening classes ($\mu_1$) is lower than the mean test - score of students in the morning classes ($\mu_2$).

Step2: Determine the alternative hypothesis

The alternative hypothesis $H_a$ represents the claim. Since the claim is $\mu_1<\mu_2$, this is the form of the alternative hypothesis. The null hypothesis $H_0$ is the statement of no difference, which is $\mu_1 = \mu_2$.

Answer:

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$H_0:\mu_1=\mu_2$
$H_a:\mu_1 < \mu_2$