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

User Rcarvalho
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Answer:

No, because the population mean, μ, is not included within the confidence interval estimate.

Explanation:

A (1 - α)% confidence interval for a population parameter can be used make inferences about a statistic test of the parameter.

Decision rule:

If the null value of the population parameter is included in the interval then the null hypothesis will not be rejected. And vice-versa.

In this case, a market researcher wants to determine whether the population mean​ time customers spent on that website is 13 minutes a day or not.

The hypothesis can be defined as follows:

H₀: The population mean​ time customers spent on that website is 13 minutes a day, i.e. μ = 13.

Hₐ: The population mean​ time customers spent on that website is different from 13 minutes a day, i.e. μ ≠ 13.

The 95% confidence interval that the mean​ time customers spent on​ that website per day is, (15, 50).

The 95% confidence interval for the population mean time does no consist of the null value. Thus, the null hypothesis will be rejected.

It can be concluded that the population mean​ time customers spent on that website is not 13 minutes. Since the 95% confidence interval consist of values more than 13 minutes, it can be said that the mean​ time customers spent on that website is more than 13 minutes.

Thus, the answer is:

No, because the population mean, μ, is not included within the confidence interval estimate.

User Lafunamor
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