Question

A market researcher collects a simple random sample of customers from a population of over a million​ customers that use a home improvement website. After analyzing the​ sample, she states that she has​ 95% confidence that the mean​ time customers spent on​ that website per day is between 19 and 59 minutes. Suppose that the population mean​ time customers spent on that website is 26 minutes a day. Does this value of the population mean help to show that the confidence interval estimate is​ correct? Explain.

Answer 1

Given : A market researcher states that she has​ 95% confidence that the mean​ time customers spent on​ that website per day is between 19 and 59 minutes.

To Find :Suppose that the population mean​ time customers spent on that website is 26 minutes a day. Does this value of the population mean help to show that the confidence interval estimate is​ correct?

Solution :

Confidence interval at 95% = 19 to 59

We are given that the population mean​ time customers spent on that website is 26 minutes a day

So, Mean must be the mid point of the 95% confidence interval

Mid point =
`(19+59)/(2)=39`

Since 26 is not the mid point of the 95% confidence interval

So, this value of the population mean help to show that the confidence interval estimate is​ incorrect.