A computer manufacturing company has sent a mail survey to 2800 of its randomly selected customers that have purchased a new personal computer.The survey asked the customers whether or not they were satisfied with the computer.800 customers responded to the survey.640 customers indicated that they were satisfied,while 160 customers indicated they were not satisfied with their new computer.Construct a 96 percent confidence interval estimate of the true proportion of customers satisfied with their new computer.
A) $[ .771 \quad .829 ]$
B) $[ .788 \quad .812 ]$
C) $[ .775 \quad .825 ]$
D) $\left[ \begin{array} { l l }
.785 & .816
\end{array} \right]$

Question

A computer manufacturing company has sent a mail survey to 2800 of its randomly selected customers that have purchased a new personal computer.The survey asked the customers whether or not they were satisfied with the computer.800 customers responded to the survey.640 customers indicated that they were satisfied,while 160 customers indicated they were not satisfied with their new computer.Construct a 96 percent confidence interval estimate of the true proportion of customers satisfied with their new computer.
A) $[ .771 \quad .829 ]$
B) $[ .788 \quad .812 ]$
C) $[ .775 \quad .825 ]$
D) $\left[ \begin{array} { l l } 
.785 & .816
\end{array} \right]$

Quizplus · Accepted Answer

The sample size is 800, and 640 customers indicated that they were satisfied. So the sample proportion of satisfied customers is 640/800 = 0.8. To construct a 96% confidence interval for the true proportion of satisfied customers, we can use the formula:sample proportion +/- margin of errorwhere the margin of error is:z * sqrt((sample proportion * (1 - sample proportion)) / sample size)where z is the z-score corresponding to the desired confidence level. For a 96% confidence level, z = 2.326.Plugging in the values, we get:0.8 +/- 2.326 * sqrt((0.8 * (1 - 0.8)) / 800)= 0.8 +/- 0.029= (0.771, 0.829)Therefore, the 96% confidence interval for the true proportion of satisfied customers is (0.771, 0.829).

A Computer Manufacturing Company Has Sent a Mail Survey to 2800