Rate My Professors6 records the opinions of students about their professors according to three criteria: clarity, easiness, and helpfulness. You and your friend want to choose between two professors for your Statistics class, and you see that the average ratings of these professors are as follows, together with the number of students who have provided those ratings:

Like many organizations providing ratings and evaluations, Rate My Professors provides an average rating without any measure of the extent of variation among the students from which that average was calculated. You estimate the standard deviations in the ratings as 10% of the averages in the table (e.g., you estimate the standard deviation of Prof X’s Clarity rating to be 0.1 6 4.2 = 0.42), whereas your friend estimates them as 20% of the average.

(a) Do these different assumptions result in you and your friend coming to different conclusions (at the 0.05 significance level) about which professor is better on the three criteria given? (Give three answers, one for each criterion.)

(b) Does it make any difference if you pool your estimates of the standard deviations? (Give three answers, one for each criterion.)

(c) What percentage would the standard deviation need to be in relation to the mean for you to be just unable to distinguish between the professors at the 90% level? (Give six answers, with two significant figures of accuracy: one for each criterion in the pooled and not pooled situations.

Transcribed Image Text:

Number of Students Helpfulness Clarity Easiness 12 47 Professor X Professor Y 4.2 4.5 3.3 4.1 3.6 4.0