The admissions counselors at Brainy University believe that the freshman class t

Question

The admissions counselors at Brainy
University believe that the freshman class they have just recruited is the brightest yet. If they wanted to test this belief (that the freshmen are brighter than the other classes), what would the null and alternative hypotheses be? Is this a one- or two-tailed hypothesis test?
Population of upperclassmen. They find that the freshmen do in fact have a higher mean SAT score. However, what they are unaware of is that the sample of freshmen was not representative of all freshmen at Brainy University. In fact, the sample overrepresented those with high scores and underrepresented those with low scores.

What type of error (Type I or Type II) did the counselors make?

Explanation / Answer

H0: muf-muo=0 (Difference of mean SAT score freshmen and other classes is zero)

H1:muf-muo>0 (Freshmen have mean SAT score higher than other classes)

This is one-tailed test.

Here, the counselor has rejected null hypothesis to conclude that freshmen indeed have a higher SAT score but lately discovered that the samplle of freshmen is not representative of the true population. Therefore, here a true null hypothesis [There is no difference in mean SAT score of freshmen and other classes] is rejected. The counselor makes Type I error.

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