The alternative hypothesis for an independent-measures t test states ______.
a. There is no mean difference between the two populations being compared.
b. There is no mean difference between the two samples being compared.
c. There is a non-zero mean difference between the two populations being compared.
d. There is a non-zero mean difference between the two samples being compared.
To determine the correct answer, let's break down the question and the concepts involved.
An independent-measures t-test is a statistical test used to compare the means of two independent groups or populations. The null hypothesis for this test states that there is no mean difference between the two groups, while the alternative hypothesis states that there is a non-zero mean difference.
Now, looking at the answer choices:
a. "There is no mean difference between the two populations being compared." This aligns with the null hypothesis, not the alternative hypothesis. Eliminate this option.
b. "There is no mean difference between the two samples being compared." This also aligns with the null hypothesis, not the alternative hypothesis. Eliminate this option.
c. "There is a non-zero mean difference between the two populations being compared." This aligns with the alternative hypothesis where we expect to find a non-zero mean difference. Keep this option.
d. "There is a non-zero mean difference between the two samples being compared." This option does not accurately represent the alternative hypothesis because it mentions "samples" instead of "populations." Eliminate this option.
Therefore, the correct answer is c. "There is a non-zero mean difference between the two populations being compared."