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 274 students was x ¯ ¯ ¯ x¯ = 144 minutes. Suppose that we know that the studey time follows a Normal distribution with standard deviation σ σ = 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 z z ?

(c) Can you conclude that students do claim to study more than two hours per weeknight on the average?

(a) H 0 H0 : H a Ha : (Type in "mu" as the substitute for μ μ and "!=" for ≠ ≠ .)

(b) z z :

(c) Conclusion: (Answer with "Yes/Y" or "No/N".)

Answer 1

Solution:

Claim : more than 2 hours per night on the average

i.e. > 120 minutes.

σ = 65

n = 274

= 144

a) Hypothesis can be written as

H0 : = 120

Ha :   > 120

b)The test statistic z is given by

z =

= (144 - 120) / (65/274)

= 6.11

The value of test statistic is 6.11

c) Now , observe that ,there is > sign in Ha. So , the test is right tailed.

p value = P(Z > 6.11)

= P(Z < -6.11)

= 0.0000 (use z table)

So , we reject the null hypothesis and conclude that  students do claim to study more than two hours per weeknight on the average.

YES.