Question

You want to know the opinions of American high school teachers on the issue of

establishing a national proficiency test as a prerequisite for graduation from high

school. You obtain a list of all high school teachers belonging to the National Education

and mail a survey to a random

sample of $2500$ teachers. In all, $1347$ of the teachers return the survey. Of those who

responded, $32\%$ say that they favor some kind of national proficiency test. Which of the

following statements about this situation is true?

a. Because random sampling was used, we can feel confident that the percent of all

American high school teachers who would say they favor a national proficiency test

is close to $32\%.$

b. We cannot trust these results, because the survey was mailed. Only survey results

from face-to-face interviews are considered valid.

c. Because over half of those who were mailed the survey actually responded, we can

feel fairly confident that the actual percent of all American high school teachers who

would say they favor a national proficiency test is close to $32\%.$

d. The results of this survey may be affected by undercoverage and nonresponse.

e. The results of this survey cannot be trusted due to voluntary response bias.

Short answer

The correct option is:

d. The results of this survey may be affected by undercoverage and nonresponse.

Step-by-step solution

Given information

We have been given four options from which we have to select the correct one.

a. Because random sampling was used, we can feel confident that the percent of all

American high school teachers who would say they favor a national proficiency test

is close to $32\%$.

b. We cannot trust these results, because the survey was mailed. Only survey results

from face-to-face interviews are considered valid.

c. Because over half of those who were mailed the survey actually responded, we can

feel fairly confident that the actual percent of all American high school teachers who

would say they favor a national proficiency test is close to$32\%.$

d. The results of this survey may be affected by undercoverage and nonresponse.

e. The results of this survey cannot be trusted due to voluntary response bias.

Explanation

(a) False; the sample is not random; it is a voluntary response sample.

(b) False, non-face-to-face interviews are also accepted.

(c) False, because the rate of non-response remains high (a little less than 50 percent ).

(d) This is correct, because the non-response rate remains high (a little less than 50 percent ).

(e) False; if the voluntary response sample's non-response rate had been 100%, the results could have been trusted.