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Chapter 7: Problem 21

A school district conducts a survey to determine whether voters favor passing a bond to fund school renovation projects. All registered voters are called. Of those called, \(15 \%\) answer the survey call. Of those who respond, \(62 \%\) say they favor passing the bond. Give a reason why the school district should be cautious about predicting that the bond will pass.

Short Answer

Expert verified
The school district should be careful about predicting the bond's passage because only a small proportion (9.3%) of all registered voters have indicated they would vote in favor of the bond. Survey response rates can impact the accuracy of predictions. Non-respondents might have differing opinions, introducing bias into the prediction.

Step by step solution

01

Identify the sample and the population

In this case, the sample are the registered voters who responded to the call, and the population is all registered voters.
02

Calculate the actual percentage of voters in favor

The percentage of registered voters that responded to the call and are in favor of passing the bond needs to be calculated. This can be done by multiplying the percentage of respondents (15%) by the percentage of those in favor (62%). The calculation is \(0.15 \times 0.62 = 0.093\), or \(9.3\%\). This means that only \(9.3\%\) of all registered voters indicated they would vote in favor of the bond.
03

Analyze the bias in survey sampling

The remaining voters who didn't respond to the survey may have different opinions on the bond issue. Hence, the result of the survey might not truly represent the opinion of all registered voters. The survey may introduce a bias known as non-response bias, where respondents may be fundamentally different from non-respondents, which could skew the results.

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