Taking an SAT preparatory course is believed to improve test scores. To investigate the effects of taking a preparatory course, scores were recorded for 5 students before and and after they took the preparatory course. Does the data below suggest that a preparatory course increases test scores? Assume we want a 90% confidence level (.10) to test the claim. HINT: Assume the null hypothesis is that test scores stay the same, before and after taking the course. Also, assume the "expected" change in test scores is zero when evaluating the test statistic. To find the test statistics, you should create a new column for the "change in test score" and evaluate the mean and standard deviation of those results.
|
Student
|
Before
|
After
|
|
1
|
1200
|
1260
|
|
2
|
1100
|
1060
|
|
3
|
1050
|
950
|
|
4
|
1000
|
1000
|
|
5
|
920
|
1050
|
(a) Identify the alternate hypothesis
(b) What is the random variable (X) that we want to evaluate?
(c) Find the test statistic (show all work)
(d) Find the P-value (show all work)
(e) Is there sufficient evidence to support the claim that taking a preparatory course increases an SAT test score? Justify your conclusion.