4. The opinions of students on the dining facilities at a university were collec

Question

4. The opinions of students on the dining facilities at a university were collected during 1 week at the four din- ing centers on the campus. A total of 300 students expressed their opinions; 90, 80, 65, and 65 of the fresh- man to senior classes, respectively. The 4000 students consisted of approximately equal numbers in each class. (a) Are the estimates from this type of survey valid for the 4000 students? (b) Can the responses be generalized separately to each of the four classes? (c) Instead of the above procedure, how would one plan to obtain the opin- ions from a sample of 300 students? To estimate the average expenses of approximately 4000

Explanation / Answer

Answer to part a)

The sample size is 300, and the population size is 4000

This implies that the sample size is less than 10% of the population size

Thus it is a valid sample and the estimates can be considered valid for the 400 students

.

Answer to part b)

The contribution from each class in the sample is different, and hence the results cannot be generalized.

In order to generalize the results to each of the four classes, the sample must contain proportional number of subjects from each of the class.

.

Answer to part c)

The best way to select the subjects is to select subjects from each class proportional to the size of each class. This will provide the true representation of the population and provide much more appropriate estimates about the complete population, and generalization of the results to each of the class would also be possible

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