Question

Teaching Ability In a sample survey of professors at the University of Nebraska, \(94 \%\) of them descrihed themselves as "ahove average" teachers. \({ }^{28}\) (a) What is the sample? What is the population? (b) Based on the information provided, can we conclude that the study suffers from sampling bias? (c) Is \(94 \%\) a good estimate for the percentage of above-average teachers at the University of Nebraska? If not, why not?

Short answer

(a) The sample is the group of professors at the University of Nebraska surveyed. The population is all professors at the University of Nebraska. (b) We don't have information to conclude if the study suffers from sampling bias. (c) The percentage \(94 \%\) may not be a good estimate for the percentage of above-average teachers at the University of Nebraska, as this is based on the professors' self-perception and could be subject to bias.

Step-by-step solution

Identify Sample and Population

The sample is the group of professors at the University of Nebraska surveyed. The population is all professors at the University of Nebraska.

Determine Sampling Bias

Sampling bias occurs when certain groups are over- or under-represented in the sample. Based on the information provided in the exercise, we don't know how the survey was conducted to conclude if the study suffers from sampling bias.

Evaluate the Estimation

The figure of \(94 \%\) represents the percentage of professors who describe themselves as 'above average'. This doesn't necessarily equate to the actual percentage of above-average teachers at the University of Nebraska. Factors like self-perception and bias could impact this statistic, making it potentially unreliable as an estimate of the actual proportion of above-average teachers.