A test preparation claims that more than 50% of the students who take their test prep course improve their scores by at least 10 points. Instead of advertising the percentage of customers who improve by at least 10 points, a manager suggests testing whether the mean score improves at all. For each customer they record the difference in score before and after taking the course. Required:
a. State the null and alternative hypotheses.
b. The P-value from the test is 0.65. Does this provide any evidence that their course works?
c. From part b, what can you tell, if anything, about the mean difference in the sample scores?

Step-by-step explanation:

Corresponding scores before and after taking the course form matched pairs.

The data for the test are the differences between the scores before and after taking the course.

μd = scores before taking the course minus scores before taking the course.

a) For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

b) We would assume a significance level of 0.05. The P-value from the test is 0.65. The p value is high. It increases the possibility of accepting the null hypothesis.

Since alpha, 0.05 < than the p value, 0.65, then we would fail to reject the null hypothesis. Therefore, it does not provide enough evidence that scores after the course are greater than the scores before the course.

c) The mean difference for the sample scores is greater than or equal to zero

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