Question

SmArT Academy, an SAT test prep company, claims that their program improves student scores). A simple random sample of 37 students took the SAT before taking the prep course and then again after taking the prep course. The average increase in their scores after taking the course was 40 points with a standard deviation of 120 points. What can we conclude about the SmArT Academy’s claim that the course improves scores? Use a significance level of α = 0.05 and the P-value method.

1. (a) What is the appropriate distribution (normal or t) to use for our calculations?

2. (b) State the null and alternate hypothesis. Is the alternate hypothesis left, right, or two-tailed?

(c) Give the significance level, α. What does this value represent?

(d) Compute the test statistic.

(e) Compute the P-value of the test statistic. What does this value represent?

6. (f) Indicate the position of the test statistic and draw the regions representing α and the P-value in the figure below.

   d

7. (g) Determine whether to reject the null hypothesis. Make sure to indicate criteria you are using to make this determination.

(h) State your conclusions in plain English.

Answer 1