Question

respondus.
state university offers several sections of a business statistics course in an in - class and online format. both formats are administered the same final exam each year. you have been assigned to test the hypothesis that the average final exam score of in - class students is different from the average final exam score of online students. the given data summarizes the sample statistics for the final exam scores for students from each format. assume that the population variances are unequal.
if population 1 is defined as in - class format and population 2 is defined as online format, then what is the correct hypothesis statement for this hypothesis test?
a. ( h_0:mu_2-mu_1geq0;h_1:mu_2 - mu_1lt0 )
b. ( h_0:mu_1-mu_2 = 0;h_1:mu_1-mu_2geq0 )
c. ( h_0:mu_1-mu_2 = 0;h_1:mu_1-mu_2
eq0 )
d. ( h_0:mu_1-mu_2leq0;h_1:mu_1-mu_2gt0 )

Explanation:

To determine the correct hypothesis statement, we analyze the problem: we want to test if the average final exam score of in - class (Population 1, \(\mu_1\)) students is different from that of online (Population 2, \(\mu_2\)) students.

• The null hypothesis (\(H_0\)) for a test of difference between two means (when we are testing for a difference, not a specific direction like greater than or less than) is that there is no difference between the two population means. Mathematically, this is \(H_0:\mu_1 - \mu_2=0\) (because if \(\mu_1=\mu_2\), then \(\mu_1-\mu_2 = 0\)).
• The alternative hypothesis (\(H_1\)) is that there is a difference between the two population means. Since we are testing for a difference (not a one - tailed test like greater than or less than), the alternative hypothesis is \(H_1:\mu_1-\mu_2

eq0\).

Now let's analyze each option:

• Option A: The null and alternative hypotheses are set up with \(\mu_2-\mu_1\), which is not consistent with our definition of Population 1 (in - class) and Population 2 (online) and the test for difference. Also, the direction (less than in alternative) is incorrect as we are testing for a difference, not a one - tailed test in this direction.
• Option B: The alternative hypothesis is a one - tailed test (\(\mu_1 - \mu_2>0\)), but we are testing for a difference (two - tailed), so this is incorrect.
• Option C: The null hypothesis is \(H_0:\mu_1-\mu_2 = 0\) (no difference) and the alternative hypothesis is \(H_1:\mu_1-\mu_2

eq0\) (there is a difference), which matches our analysis.

• Option D: The null hypothesis is a one - tailed test (\(\mu_1-\mu_2\leq0\)) and the alternative is also a one - tailed test (\(\mu_1 - \mu_2>0\)), which is not consistent with testing for a difference between the two means.

Answer:

C. \(H_0:\mu_1 - \mu_2 = 0; H_1:\mu_1-\mu_2
eq0\)