Question

sampling all listed residential telephone numbers in the United States. Of 45,956 calls to these numbers, $5029$ were completed. The goal of the survey was to estimate how far people drive, on average, per day.$14$

(a) What was the rate of nonresponse for this sample?

(b) Explain how nonresponse can lead to bias in this survey. Be sure to give the direction of the bias.

Short answer

Part (a) The rate of non-response is $89.06\%$

Part (b) Underestimation bias.

Step-by-step solution

 Part (a) Step 1: Given information

Number of calls made, $n=45956$

Number of calls completed, $c=5029$

Part (a) Step 2: Concept

A simple random sample (SRS) of size n is made up of $n$people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Total number of calls $=45,956$

Number of responded $=5029$

To begin, determine the number of unanswered calls.

Not responded = Total number of calls- Number of responses.

Not responded $=45,956-5029=40927$

Therefore, the rate of non-response is,

$$\begin{gathered} =\frac{Notresponded}{Totalnumberofcalls} \\ =\frac{40927}{45956}=0.8906=89.06\% \end{gathered}$$

Part (b) Step 1: Explanation

Total number of calls$=45,956$

Number of responded $=5029$

The rate of non-response is $89.06\%$

A household telephone was utilized for the survey. As a result, a large number of people may be working away from home. That persons are not used as a sample, resulting in estimation bias.