A test of the null hypothesis that the average college student gains 15 pounds during the first year at college surveyed a random sample of 100 students and obtained a sample mean of 4.82 pounds with a standard deviation of 5.96 pounds. Explain why you either agree or disagree with each of these conclusions:

a. “We assumed that the standard deviation of our sample equaled the population standard deviation.”

b. “We calculated the t value to be −17.08. The two-sided P value is 2.82 × 10⁻³¹.

According to Fisher’s rule of thumb, our data are not statistically significant because our P value is considerably less than 0.05. This indicates that the probability of observing a large difference between the sample mean and the null hypothesis is greater than 0.05.”

c. “Our data strongly indicate that the Freshman 15 is just a myth. However, it must be recognized that we only took one sample of 100 students. Perhaps, if we took other samples, our results would be different.”