An article in the San Jose Mercury News stated that students in the California state university system.

Question

An article in the San Jose Mercury News stated that students in the California state university system take 5 years, on average, to finish their undergraduate degrees. A freshman student believes that the mean time is less and conducts a survey of 68 students. The student obtains a sample mean of 4.5 with a sample standard deviation of 1.8. Is there sufficient evidence to support the student's claim at an a=0.05 significance level?

Determine the test statistic.

Find the p-value.

Answer 1

I'll first put on here the null and alternative hypotheses. Because the student believes the mean time to be less than 5, this is your alternative.

H₀: µ=5

H₁: µ<5

Now for your test statistic, since we don't have the population standard deviation, we'll be getting a t test statistic (not z). Since there are 68 students surveyed, we have 67 degrees of freedom So we can set the test statistic up as follows:

t = (4.5 - 5)/(1.8/√(68)) = -2.29

Because the question asks for p-value, we can find this using a calculator. This would either be T.DIST(-2.29, 67) in Excel or tcdf(lower=-100, upper=-2.29, df=67) on a TI-84. In either case, this will get you a p-value of 0.0126. Since this is less than α=0.05, you'll be rejecting the null hypothesis and concluding that there is sufficient evidence to support the student's claim of fewer than 5 years to complete their degrees.