Question

An opinion poll calls $2000$randomly chosen residential telephone numbers, then asks to speak with an adult member of the household. The interviewer asks, “Box office revenues are at an all-time high. How many movies have you watched in a movie theater in the past $12$months?” In all, $1131$people responded. The researchers used the responses to estimate the mean number of movies adults had watched in a movie theater over the past $12$months.

a. Describe a potential source of bias related to the wording of the question. Suggest a change that would help fix this problem.

b. Describe how using only residential phone numbers might lead to bias and how this will affect the estimate.

c. Describe how nonresponse might lead to bias and how this will affect the estimate.

Short answer

Part a. A possible change would be to shorten the time from $12to3$months or even to one month as people are then more likely to remember the exact number of times they went to the movies compared to using a long period such as a year

Part b. This would then most likely lead to an overestimation of the actual mean number of movies as people who do not own a phone are more likely to be poorer people and poorer people are less likely to be able to afford going to the movies.

Part c. This would then most likely lead to an underestimation of the actual mean number of movies as people who are not at home when they phone are more likely to have been at the movies and are more likely to go out frequently.

Step-by-step solution

Part a. Step 1. Explanation

The survey has possible response bias because if people go often to the movies then they most likely don/t know the exact number of times that they went to movies in the past twelve months and thus they will have to estimate the amount.

A possible change would be to shorten the time from$12to3$ months or even to one month as people are then more likely to remember the exact number of times they went to the movies compared to using a long period such as a year.

Part b. Step 1. Explanation

The survey has possible selection bias because the people in the survey were only phoned while there are people in the survey were only phoned while there are people who do not have telephone and thus some people in the population will be excluded.

This would then most likely lead to an overestimation of the actual mean number of movies as people who do not own a phone are more likely to be poorer people and poorer people are less likely to be able to afford going to the movies.

Part c. Step 1. Explanation

The survey has possible non-response bias because some people who were phoned might not have picked up the phone or some people did not complete the survey.

This would then most likely lead to an underestimation of the actual mean number of movies as people who are not at home when they phone are more likely to have been at the movies and are more likely to go out frequently.