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 α=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 μd 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: μd>0 H1: μd≤0
B. H0: μd<0 H1: μd≥0
C. H0: μd≥0 H1: μd<0
D. H0: μd≤0 H1: μd>0
E. H0: μd=0 H1: μd≠0
F. H0: μd≠0 H1: μd=0
b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using α=0.01. The test statistic is nothing. (Round to two decimal places as needed.) The critical value(s) is(are) nothing. (Use a comma to separate answers as needed. Round to two decimal places as needed.) Interpret the results of the hypothesis test. Since the test statistic does not fall between falls between is greater than is less than the critical value(s), reject do not reject the null hypothesis. There is sufficient insufficient evidence that the mean score is higher after the review course.
c. Identify the p-value and interpret the result. p-value=nothing (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 sufficient insufficient 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 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. B. 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. 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 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.