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 463463 students was ?¯=13.7x¯=13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation ?=7.4σ=7.4 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 1313 hours per week on the average?

You may find Table A helpful.

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

?0:?=13 hours ; ??:?≠13 hoursH0:μ=13 hours ; Ha:μ≠13 hours

?0:?=13 hours ; ??:?>13 hoursH0:μ=13 hours ; Ha:μ>13 hours

?0:?=13 hours ; ??:?<13 hoursH0:μ=13 hours ; Ha:μ<13 hours

?0:?=13 hours ; ??:?=13 hoursH0:μ=13 hours ; Ha:μ=13 hours

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

z=

(c) What is the P ‑value of the test?

between 0.001 and 0.005

less than 0.0001

larger than 0.05

between 0.020 and 0.030

Can you conclude that students do claim to study more than 13 hours per week on average?

No, the large ?P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

No, the small ?P ‑value is strong evidence that students do not claim to study more than 13 hours per week on average.

Yes, the small ?P ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

Yes, the large ?P ‑value is strong evidence that students do claim to study more than 13 hours per week on average.

Answer 1

solution:

sample size = n = 463

sample mean = = 13.7 hrs.

population standard deviation = = 7.4 hrs.

claim: that the student study more than 13 hrs.

so the correct null and alternative hypothesis will be :

hrs

hrs.

it is a right tailed test

b)

since population standard deviation is known and sample size als o large enough, so we will use z test statistics:

test statistics:

z score = 2.04

c)

p value = 1 - value of z to the left of 2.04 = 1 - 0.9793 = 0.0207

p value is between 0.020 and 0.030

d)

No, small p value is strong evidence that students do not claim to study more than 13 hours per week on average.