Question

You want to know the mean number of customers that enter a store per hour. Using data collected over the last month, we have

* a 90% confidence interval (C.I.) for the population mean is (17.11, 24.75)

* a 99% C.I. of (14.95, 26.91)

* a 95% C.I. of (16.38,25.48)

For a hypothesis test of H0: μ = 25, in what range will the P value be?

Explain. Just use the CI’s to determine the range p-value should be in.

Answer 1

The range of p-value is: 0.05 < p-value < 0.10 [ANSWER]

Explanation:

Since, the value μ = 25 does not lie in the 90% confidence interval (17.11, 24.75)

=> p-value < Significance level (Since, at the specified significance level H0: μ = 25 will be rejected)

=> p-value < 100% - 90%

=> p-value < 10%

=> p-value < 0.10 .................(1)

Since, the value μ = 25 lies in the 99% confidence interval (14.95, 26.91)

=> p-value > Significance level (Since, at the specified significance level H0: μ = 25 will not be rejected)   

=> p-value > 100% - 99%

=> p-value > 1%

=> p-value > 0.01 .................(2)

Since, the value μ = 25 lies in the 95% confidence interval (16.38,25.48)

=> p-value > Significance level (Since, at the specified significance level H0: μ = 25 will not be rejected)   

=> p-value > 100% - 95%

=> p-value > 5%

=> p-value > 0.05 .................(3)

From equations (1), (2) and (3), we get:

0.01 < 0.05 < p-value < 0.10

=> 0.05 < p-value < 0.10 [ANSWER]

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