Suppose 5000 Students Are Randomly Assigned to Either Take an SAT

Suppose 5000 students are randomly assigned to either take an SAT coaching course or not, with the following results in their improvements in SAT scores:
A $99 \%$ confidence interval for the difference in population means turns out to be $(0.72,2.88)$ .
a. Based on this interval, would you reject the null hypothesis that the population means are equal at the .01 significance level? (No explanation is needed.)
b. Which is the more appropriate conclusion to draw: (i) that the data provide very strong evidence that the population means differ, or (ii) that the data provide evidence that the population means differ substantially? (No explanation is needed.)

Correct Answer:

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a. Yes. Because the interval does not in...

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