Question

it is believed that the mean weight gain for college freshmen is 5 pounds. a researcher is interested in determining if freshmen in the southeast gain more weight. for this study the alternate hypothesis would be: a h₁:μ < 5 b h₁:μ ≠ 5 c h₁:μ > 5

Explanation:

The null hypothesis \(H_0\) is usually the statement of no - difference or the status - quo. Here, the null hypothesis would be \(H_0:\mu = 5\) (the mean weight gain is 5 pounds as believed). The alternative hypothesis \(H_1\) is what we are trying to find evidence for. The researcher is interested in determining if freshmen in the Southeast gain more weight. So, we are looking for a one - sided (right - tailed) test. If \(\mu\) represents the mean weight gain, then the alternative hypothesis should be \(H_1:\mu>5\) (mean weight gain is greater than 5 pounds).
Option A (\(H_1:\mu < 5\)) is a left - tailed test (looking for less than 5 pounds) which is not what the researcher wants. Option B (\(H_1:\mu
eq5\)) is a two - tailed test (looking for a difference, either more or less than 5 pounds) which also does not match the researcher's interest of "more weight".

Answer:

C. \(H_1:\mu > 5\)