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.

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 = [tex]\frac{19+59}{2}=39[/tex]

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.