Suppose that 5,000 students are randomly assigned to either take an SAT coaching course or not, with the following results in their improvements in SAT scores:

a. Use technology to conduct a test of whether the sample data provide evidence that SAT coaching is helpful. State the hypotheses and report the test statistic and p-value. Draw a conclusion in the context of this study.
b. Use technology to produce a 99% CI for the difference in population mean improvements between the two groups. Interpret this interval.
c. Are the test conclusion and CI consistent with each other? Explain.
d. Do the sample data provide very strong evidence that SAT coaching is helpful? Explain whether the p-value or the CI helps you to decide.
e. Do the sample data provide strong evidence that SAT coaching is very helpful? Explain whether the p-value or the CI helps you to decide.
f. Comment on what this exercise reveals about the distinction between statistical significance and practical importance.

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Sample Sample Sample size SD mean Coaching group 14.40 2,500 46.20 Control group 44.40 15.30 2,500