A math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of theexam, scores are normally distributed with =523. The teacher obtains a random sample of 2000 students, puts them through the reviewclass, and finds that the mean math score of the 2000 students is 531 with a standard deviation of 117. Complete parts(a) through(d) below.

(a) State the null and alternative hypotheses. Let be the mean score. Choose the correct answer below.

A.

H0:>523, H1:523

B.

H0:<523, H1:>523

C.

H0:=523, H1:>523

D.

H0:=523, H1:523

(b) Test the hypothesis at the =0.10 level of significance. Is a mean math score of 531 statistically significantly higher than 523? Conduct a hypothesis test using theP-value approach.

Find the test statistic.

t0=________(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is______(Round to three decimal places asneeded.)

Is the sample mean statistically significantlyhigher?

No

Yes

(c) Do you think that a mean math score of 531 versus 523 will affect the decision of a school admissionsadministrator? In otherwords, does the increase in the score have any practicalsignificance?

No, because the score became only 1.53% greater.

Yes, because every increase in score is practically significant.

(d) Test the hypothesis at the =0.10 level of significance with n=350 students. Assume that the sample mean is still 531 and the sample standard deviation is still 117. Is a sample mean of 531 significantly more than 523? Conduct a hypothesis test using theP-value approach.

Find the test statistic.

t0=______(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is_______(Round to three decimal places asneeded.)

Is the sample mean statistically significantlyhigher?

No

Yes

What do you conclude about the impact of large samples on theP-value?

A.

As nincreases, the likelihood of not rejecting the null hypothesis increases.However, large samples tend to overemphasize practically insignificant differences.

B.

As nincreases, the likelihood of not rejecting the null hypothesis increases.However, large samples tend to overemphasize practically significant differences.

C.

As nincreases, the likelihood of rejecting the null hypothesis increases.However, large samples tend to overemphasize practically insignificant differences.

D.

As nincreases, the likelihood of rejecting the null hypothesis increases.However, large samples tend to overemphasize practically significant differences.