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Suppose at a large high school, the average AP test score for AP Statistics is $2.84$ with a standard deviation of $0.45$.

The school decided to offer nightly study sessions and randomly chose $30$ students to participate. These $30$ students averaged AP scores of $3.1$.

What can be said about the effectiveness of the AP study sessions?

A

Nothing, since the design of the experiment was not done in an effective manner.

B

Nothing, since the sample size is too small to develop any reasonable conclusions.

C

The students in the study sessions did not perform much better than their peers; their effort is only $0.58$ standard deviations above the mean of their peers.

D

These students performed much better than their peers; their results are $3.16$ standard deviations above the mean of their peers.

E

While this study shows that these $30$ students did better than their peers, it would have been more effective to compare these students’ scores to the national AP average.

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