The owner of a local chain of grocery stores is always trying to minimize the ti

Question

The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 11.6 minutes. and a standard deviation of 2.6 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 26 customers visiting her store this week resulted in a mean of 10.5 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 11.6 minutes? Use = .02.

(a) Find z. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer correct to four decimal places.)

(b) State the appropriate conclusion.

Reject the null hypothesis, there is not significant evidence that the mean checkout time is less than 11.6 minutes.Reject the null hypothesis, there is significant evidence that the mean checkout time is less than 11.6 minutes.    Fail to reject the null hypothesis, there is significant evidence that the mean checkout time is less than 11.6 minutes.Fail to reject the null hypothesis, there is not significant evidence that the mean checkout time is less than 11.6 minutes.

Explanation / Answer

The corresponding test and z-value to the given scenerio is

a) z- value = -2.16

P-value = 0.0155

b) Appropriate conclusion :

Reject the null hypothesis, there is significant evidence that the mean checkout time is less than 11.6 minutes.

Z Test of Hypothesis for the Mean Data Null Hypothesis                    m= 11.6 Level of Significance 0.02 Population Standard Deviation 2.6 Sample Size 26 Sample Mean 10.5 Intermediate Calculations Standard Error of the Mean 0.509901951 Z Test Statistic -2.157277487 Lower-Tail Test Lower Critical Value -2.053748911 p-Value 0.015492025 Reject the null hypothesis

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