Question

A class survey in a large class for first-year college students asked, "About how many minutes do you study on a typical weeknight?" The mean response of the 284 students was x⎯⎯⎯x¯ = 138 minutes. Suppose that we know that the studey time follows a Normal distribution with standard deviation σσ = 65 minutes 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 2 hours per night on the average?

(a) State null and alternative hypotheses in terms of the mean study time in minutes for the population.
(b) What is the value of the test statistic zz?
(c) Can you conclude that students do claim to study more than two hours per weeknight on the average?

Answer 1

a) Null and alternative hypotheses

Ho : = 120 min

H1 : > 120 min

b) test statistic Z

Z = ( xbar - )/(/√n)

Z = ( 138 - 120)/(65/√284)

Z test statistic = 4.67

c) Zcritical for a = 0.05 and right tailed test

Zcritical = Z​​​​​​1-0.05 = Z​​​​​​0.95

Zcritical = 1.645

Here Z = 4.67 > 1.645 , we reject Ho

Conclusion : There is sufficient evidence to conclude that students do claim to study more than two hours per weeknight on the average