Chapter 4: Q T4.11. (page 275)

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 Association (the country’s largest teachers’ union) 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) Since random sampling was used, we can feel confident that the percentage 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 pretty 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 nonresponse bias.
(e) The results of this survey cannot be trusted due to voluntary response bias.

Short Answer

Expert verified

The correct option is (d) The results of this survey may be affected by nonresponse bias.

Step by step solution

Given information

A study was done to learn about the perspectives of American high school teachers on the creation of national proficiency examinations.

Concept

Non-sampling mistakes, on the other hand, are the most significant errors in even the most meticulous surveys. These have nothing to do with selecting a sample and can be found in any census. Nonresponse is the single biggest issue with a sample: people can't be reached or refuse to respond. Response bias can occur when respondents give incorrect replies. Finally, the precise wording of questions has a significant impact on the responses.

Explanation

A study was done to learn about the perspectives of American high school teachers on the introduction of national proficiency examinations. This survey was conducted by sending emails to $2500$ instructors, of whom $1347$ responded, with just $32 %$ 32% of those responding in favour of the test. Nonresponse bias occurs when the sample units chosen for the survey or experiment fail to reply because they are incapable, unavailable, or unwilling to do so. It reduces the sample size in general. The response rate is low in this situation, which may have an impact on the survey's outcome. As a result, it's possible that the survey's results will be influenced by nonresponse bias. As a result, the proper selection