I need help finding the test statistic z

A class survey in a large class for first-year college students asked, "About how many hours do you study during a typical week?" The mean response of the 499 students was x = 15.3 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation σ = 8.5 hours in the population of all first-year students at this university.

Regard these students as an SRS from the population of all first-year students at this university. Does the study give good evidence that students claim to study more than 15 hours per week on the average?

I have set up the hypotheses as H0: μ = 15 hrs and Ha: μ > 15 hrs. After that, I must find the test statistic Z. What I have been doing is (15-15.3)/8.5. I am not sure what I am doing wrong.

• You need to include the self study tag. – Michael R. Chernick Dec 2 '17 at 20:57

1 Answer

You're not doing anything wrong. The Z score is .04. That means the class scored .04 s.d. above the population mean. And thus the difference is not statistically significant.