Question

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 468 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?

(a) State null and alternative hypotheses in terms of the mean study time in hours for the population.

(b) What is the value of the test statistic z? (Give your answer to two decimal places.)

(c) What is the P-value of the test?

Answer 1

(a)

H0: Null Hypothesis: 15 ( Students claim to study not more than 15 hours per week on the average)

HA: Alternative Hypothesis: 15 ( Students claim to study more than 15 hours per week on the average) (Claim)

(b)

= 15.3

= 8.5

n = 468

Test Statistic is given by:

So,

the value of the test statistic z = 0.76

(c)

By Technology, P - value = 0.2226

So,

the P-value of the test = 0.2226