Chapter 8.2, Problem 54E

a)

To determine

To estimate confidence level.

Answer to Problem 54E

The confidence level = 87.88%

Explanation of Solution

Given:

  $\begin{array}{l}n=5594\\ x=3547\\ E=1\%=0.01\end{array}$

Formula:

Sample proportion:

  $\widehat{p}=\frac{x}{n}$

Margin of error:

  $E=Z_{\alpha /2}\times \sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}$

The sample proportion is,

  $\widehat{p}=\frac{3547}{5594}=0.6341$

Using the formula,

  $\begin{array}{l}0.01=Z_{\alpha /2}\times \sqrt{\frac{0.6341(1-0.6341)}{5594}}\\ Z_{\alpha /2}=\frac{0.01}{0.00644}=1.55\end{array}$

Therefore,

We need to determine the probability that,

  $\begin{array}{l}P(-1.55<Z<1.55)=P(Z<1.55)-P(Z<-1.55)\\ P(-1.55<Z<1.55)=0.9394-0.0606\\ P(-1.55<Z<1.55)=0.8788=87.88\%\end{array}$

Hence, confidence level is 87.88%

b)

To determine

To explain bias in the study.

Answer to Problem 54E

The non-response bias.

Explanation of Solution

Given:

  $\begin{array}{l}n=1028\\ \widehat{p}=64\%=0.64\\ E=3\%=0.03\end{array}$

The non-sampling biases are: selection bias, response bias and non-response bias. From this biases, non-response bias is the results of not having a data for everybody in the sample. Therefore, the results cannot be generalized as we are not sure that those of who we have data will represent those of who we do not have data.