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

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

Expert verified

a. A potential source of bias related to the wording of the question is response bias, shortening the time from 12to3month.

b. Using only residential phone numbers might lead to bias and how this will affect the estimate is selection bias is an overestimation.

c. The nonresponse might lead to bias and how this will affect the estimate is nonresponse bias is the underestimation.

Step by step solution

01

Part (a) step 1: Given Information

We need to describe a potential source of bias related to the wording of the question.

02

Part (a) step 2: Explanation

TYPES OF BIAS
Select or undercoverage bias will exclude part of the population.
Measurement of response bias will use a method that gives different values from the true value.
The nonresponse bias is a result of not having data for everybody in the sample.

SOLUTION
The survey has possible response bias, because if people go often to movies, then they likely don't know the exact number of times that they went to movies in the past 12months, and thus they will have to estimate this amount (which could lead to response bias).

A possible change would be to shorten the time from 12to3months or even to 1months, as , mere like to remember the exact number of times they went to the movies compared to use a long period as a year.

03

Part (b) step 1: Given Information

We need to describe how using only residential phone numbers might lead to bias and how this will affect the estimate.

04

Part (b) step 2: Explanation

TYPES OF BIAS
Select or undercoverage bias will exclude part of the population.
Measurement of response bias will use a method that gives different values from the true value.
The nonresponse bias is a result of not having data for everybody in the sample.

SOLUTION

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

Here, 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 poor people and poorer people are less likely to be able to afford to go to the movies.

05

Part (c) step 1: Given Information

We need to describe that how nonresponse might lead to bias and how this will affect the estimate.

06

Part (c) step 2: Explanation

TYPES OF BIAS
Select or undercoverage bias will exclude part of the population.
Measurement of response bias will use a method that gives different values from the true value.
The nonresponse bias is a result of not having data for everybody in the sample.

SOLUTION

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

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