Question

Hypothesis testing: A student group claims that first-year students at a university must study 2.25 hours per night during the school week. A skeptic suspects that they study less than that on average. A class survey finds the study time claimed by 259 students is 147 minutes. Regard these students as a random sample of all 1st year students and suppose what study times follow a Normal Distribution with a population standard deviation 62 minutes. Test to see if the students study less than 150 minutes per night.

Also, what do you conclude at the 10% significance level? Please explain as I am lost on this.

Answer 1

Null Hypothesis, 150

Alternative Hypothesis, 150

Test statistic,

z = (147 - 150)/(62/sqrt(259))
z = -0.78

p-value = P(z < -0.78)
p-value = 0.2177

As p-value > 0.1, fail to reject H0

Here the significance level, 0.1. This is right tailed test; hence rejection region lies to the right. -1.28 i.e. P(z < -1.28) = 0.01

Reject H0 if test statistic, z < -1.28

There is not sufficient evidence to conclude that the the students study less than 150 minutes