Question

The population mean wait time to check out of a supermarket has been 10.73 minutes. Recently in an effort to improve the waiting time, the supermarket has experimented with a system in which there is a single waiting line with multiple checkout servers. A sample of 25 customers was selected, and their mean wait time to check out was 12.1 minutes. Assume a population standard deviation of 5.8 minutes. At the 0.05 level of significance, is there evidence that the population mean wait time to check out is more than 10.73 minutes?

Solve using the p-value method AND Solve using the critical value method

Answer 1

The null and alternative hypothesis are-

Null hypothesis,

Alternative hypothesis,

At a given significance level of we need to test the hypothesis.

We have given the information for randomly selected customers and their mean wait time to check out is given as also we have given the population standard deviation .

the test we use for hypothesis testing is One sample Z test and the test statistic is given by-

Calculation of test-statistic:

So the test statistic is calculated as

Using P-value method:

P-value: Since we are testing a right-tailed hypothesis and the significance level is given as , then the p-value for the test-statistic is calculated as -

So the p-value for the test statistic is calculated as

Decision: We reject the null hypothesis if

Since

Conclusion: At significance level sample data provides insufficient evidence to reject null hypothesis, hence, "We fail to reject null hypothesis "

In other words, we conclude that the true mean wait time to check out of a supermarket is .

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Using Critical value method:

For the given significance level of the critical value is -

Decision: We reject the null hypothesis if

Since,

Conclusion: At significance level sample data provides insufficient evidence to reject the null hypothesis, hence, "We fail to reject null hypothesis and conclude that the true mean wait time to check out of a supermarket is "

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So using both the p-value and critical value method we came to the same conclusion of FTR(Fail to reject) null hypothesis .