Question

Researchers report that on average, freshmen who live on campus gain 15 pounds during their first year in college. You survey 10 of your friends and find that the average weight gain the first year was 16.2 lbs (s.d. = 2.6). How does weight gain among your friends compare to the national average?

What is the correct statistical test?

a) single-sample z-test

b) single-sample t-test

c) z-test for proportions

Answer 1

Objective : To compare the sample average or mean to the hypothsized population mean (National Average)

Here, given that Sample size (n) = 10, Sample mean ( $\overline{x}$ ) = 16.2 and Sample Standard deviation (s) = 2.6

To test: H₀: $\mu =15$ Vs H_a : $\mu \neq15$

Since, we are comparing the means, we would not use c) z-test for proportions in this case.

Now, to make a decision between single-sample z-test an t test, we would check if the population standard deviation is known. If known, we use z test, otherwise, we would go for  single-sample t-test.

In our case, since the population standard deviation ( $\sigma$ ) is not known, the correct statistical test is:

b) single-sample t-test.