Night Owls ~A MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual proportion of MSU students who regularly sleep less than 8 hours each night isless thanthe value reported by the MSU psychologist. She randomly selects 202 students and asks them, "Do you regularly sleep less than 8 hours each night?" She finds that 69 of the 202 students answered "yes" to the question.1.Which one of the following statements about the number 40% is correct?A. It is a claimed parameter.

B. It is a sample statistic.

C. It is a margin of error.

D. It is a standard error.

2.Choose the null and alternative hypotheses Cindy should use to test her theory.A.

0

:=0.4

H0:p=0.4,

:

<0.34

HA:p^<0.34

B.

0

:=0.4

H0:p=0.4,

:<0.4

HA:p<0.4

C.

0

:=0.4

H0:p=0.4,

:0.4

HA:p0.4

D.

0

:

=0.4

H0:p^=0.4,

:

>0.4

HA:p^>0.4

3.If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test?A. 30

B. 26

C. 20

D. 10

E. 69

F. None of the above

4.Calculate the test statistic.=

z=

5.Calculate the p value.=

p=

6.Which of the following describes the probability represented by the p-value for this test?A. It is the probability that 40% of all MSU students regularly sleep less than 8 hours a day, assuming the null model is valid.

B. It is the probability that any random sample of 202 MSU students would have 34.16% saying they regularly sleep less than 8 hours a day.

C. It is the probability that less than 40% of MSU students regularly sleep less than 8 hours a day if, in fact, 34.16% actually do.

D. It is the probability that a random sample of 202 MSU students would result in 34.16% or fewer who regularly sleep less than 8 hours a day, assuming the null model is valid.

E. None of the above.