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 463 students was ?¯=13.7 hours. Suppose that we know that the study time follows a Normal distribution with standard deviation ?=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 13 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.

A. ?0:?=13 hours ; ??:?=13 hours

B. ?0:?=13 hours ; ??:?≠13 hours

C. ?0:?=13 hours ; ??:?<13 hours

D. ?0:?=13 hours ; ??:?>13 hours

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

?=

(c) What is the ? ‑value of the test?

A. between 0.001 and 0.005

B. less than 0.0001

C. larger than 0.05

D. between 0.020 and 0.030

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

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

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

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

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

Answer 1

Here we have given that,

Claim: To check whether all the first year students study more than 13 hours per week on the average.

(A)

The Null and Alternative Hypothesis is as follows

v/s

That is here option D is correct.

We have given that,

n= Number of Students=463

= sample mean of students reponses =13.7 Hours

= population standard deviation = 7.4 Hours

(B)

Now, we can find the test statistic

= 2.04

we get,

the Test statistic is 2.04

(C)

Now we find the P-value

= level of significance=0.05

This is Right (one) tailed test

Now, we can find the P-value

P-value =(P(Z > z)

=[1- P( Z < 2.04) ]

=[ 1 - 0.9773 ] using standard normal z probability table

= 0.0227

we get the P-value is 0.0227

Here This P-value is lies between 0.020 and 0.030

that is here optoin D is correct.

(D)

Decision:

P-value < 0.05 ()

That is we reject Ho (Null Hypothesis)

Conclusion:

There is the sufficient evidence that all the first year students study more than 13 hours per week on the average.

Here Option D is correct.

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