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,.829]
B)[.788,.812]
C)[.775,.825]
D)[.785,.816]

Question

Quizplus · Accepted Answer

First, we calculate the point estimate for the proportion of satisfied customers:

p̂ = 640/800 = 0.8

Next, we calculate the standard error of the proportion:

SE = sqrt(p̂(1-p̂)/n) 
SE = sqrt(0.8(1-0.8)/800) 
SE = 0.018

To find the 96% confidence interval, we need to find the critical value from the t-distribution. Since we have a large enough sample size (800), we can use the Z-distribution instead. The critical value for a 96% confidence interval with a two-tailed test is 1.96.

Now we can construct the confidence interval:

CI = p̂ ± Z*SE 
CI = 0.8 ± 1.96*0.018 
CI = 0.8 ± 0.035

Therefore, the 96% confidence interval for the true proportion of satisfied customers is [0.765, 0.835].

The closest option is A) [.771, .829], which is within the range of our calculated confidence interval. Therefore, the best choice is A).

A Computer Manufacturing Company Has Sent a Mail Survey to 2800