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 =522. The teacher obtains a random sample of 1800 students, puts them through the reviewclass, and finds that the mean math score of the 1800 students is 527 with a standard deviation of 110. 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:=522, H1:>522

B.

H0:<522, H1:>522

C.

H0:=522, H1:522

D.

H0:>522, H1:522

(b) Test the hypothesis at the =0.10 level of significance. Is a mean math score of 527 statistically significantly higher than 522? Conduct a hypothesis test using theP-value approach.

Find the test statistic.

t0=

nothing

(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is

nothing

.

(Round to three decimal places asneeded.)

Is the sample mean statistically significantlyhigher?

Yes

No

(c) Do you think that a mean math score of 527 versus 522 will affect the decision of a school admissionsadministrator? In otherwords, does the increase in the score have any practicalsignificance?

Yes, because every increase in score is practically significant.

No, because the score became only 0.96% greater.

(d) Test the hypothesis at the =0.10 level of significance with n=400 students. Assume that the sample mean is still 527 and the sample standard deviation is still 110. Is a sample mean of 527 significantly more than 522? Conduct a hypothesis test using theP-value approach.

Find the test statistic.

t0=

nothing

(Round to two decimal places asneeded.)

Find theP-value.

TheP-value is

nothing

.

(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 rejecting the null hypothesis increases.However, large samples tend to overemphasize practically significant differences.

C.

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

D.

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

Click to select your answer(s).