A standardized test has a scale that ranges from 3 to 45. A new type of review course for the test was developed by a training company. The accompanying table shows the scores for nine students before and after taking the review course. Complete parts (a) through (d) below.

a. Perform a hypothesis test using

=0.01

to determine if the average test score is higher for the students after the review course when compared with before the course. Let

d

be the population mean of matched-pair differences for the score before the course minus the score after the course. State the null and alternative hypotheses. Choose the correct answer below.

A.

H0:

d0

H1:

d<0

Your answer is correct.

B.

H0:

d=0

H1:

d0

C.

H0:

d>0

H1:

d0

D.

H0:

d0

H1:

d=0

E.

H0:

d0

H1:

d>0

F.

H0:

d<0

H1:

d0

b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using

=0.01.

C. The critical value(s) is(are)

enter your response here.

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

nterpret the results of the hypothesis test.Since the test statistic

is less than

is greater than

does not fall between

falls between

the critical value(s),

reject

do not reject

the null hypothesis. There is

insufficient

sufficient

evidence that the mean score is higher after the review course.

Identify the p-value and interpret the result.

p-value=enter your response here

(Round to three decimal places as needed.)

Interpret the result. Since the p-value is greater than is less than the significance level, reject do not reject the null hypothesis. There is insufficient sufficient evidence that the mean score is higher after the review course.

d. What assumptions need to be made in order to perform this procedure?

A.

The samples are dependent, and the distribution of the matched-pair differences between the measurements for the population is approximately normal if the number of matched pairs is less than 30.

B.

The samples are dependent, and the distribution of the matched-pair differences between the measurements for the population is approximately uniform if the number of matched pairs is 30 or greater.

C.

The samples are independent, and the distribution of the matched-pair differences between the measurements for the population is approximately uniform if the number of matched pairs is less than 30.

D.

The samples are independent, and the distribution of the matched-pair differences between the measurements for the population is approximately normal if the number of matched pairs is 30 or greater.