The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses H0: μ = 115 Ha: μ ≠ 115. The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students.
If the researcher deems the data to be statistically significant, which of the following is true with respect to a conclusion reached?

Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 115 and standard deviation 25. A researcher suspects that incoming freshmen have a mean μ, which is different from 115, because they are often excited yet anxious about entering college. To verify her suspicion, she tests the hypotheses H0: μ = 115 Ha: μ ≠ 115. The researcher gives the SSHA to 100 incoming freshmen and observes a mean score of 119. Assume that the scores of all incoming freshmen are approximately Normal with the same standard deviation as the scores of all college students. 
 If the researcher deems the data to be statistically significant, which of the following is true with respect to a conclusion reached?

Answer

The researcher has proven that the mean SSHA score for freshmen is not 115.

Answer

The researcher has proven that the mean SSHA score for freshmen is, in fact, 115.

Answer

The researcher does not have strong enough evidence to conclude that the average freshmen SSHA score differs from that of the average SSHA score for all college students.

Answer

The researcher has strong enough evidence to conclude that the average freshmen SSHA score differs from that of the average SSHA score for all college students.

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