Taking an SAT preparatory course is believed to improve test scores. To investig

Question

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 (=0.10) 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. (3 points each, 15 points total) (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.

Explanation / Answer

The data table is not displayed.

a) H1:dbar>0 (Mean test score after the preparatory course is higher than before), where, dbar=muafter-mubefore

b) Difference in population mean test scores before and after preparatory course.

c) t=(dbar-0)/SE(dbar)

=(dbar-0)/(sd/sqrt n), where dbar is difference in mean test scores and sd is differnce in standard deviations of scores.

d) P value of t=, at df=(n-1) :

e) If p value is less than alpha=0.10, reject H0, otherwise not.

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