The waiting time to check out of a supermarket has had a population mean of 11.02 minutes.Recently,in an effort to reduce 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 50 customers was selected,and their mean waiting time to check out was 9.79 minutes with a sample standard deviation of 5.6 minutes.Complete parts(a)through(d). Click here to view page 1 of the critical values for the t distribution. Click here to view page 2 of the critical values for the t Distribution. a.At the 0.01 level of significance,using the critical value approach to hypothesis testing,is there evidence that the population mean waiting time to check out is less than 11.02 minutes? What are the null and alternative hypotheses for this test?
Question
The waiting time to check out of a supermarket has had a population mean of 11.02 minutes.Recently,in an effort to reduce 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 50 customers was selected,and their mean waiting time to check out was 9.79 minutes with a sample standard deviation of 5.6 minutes.Complete parts(a)through(d). Click here to view page 1 of the critical values for the t distribution. Click here to view page 2 of the critical values for the t Distribution. a.At the 0.01 level of significance,using the critical value approach to hypothesis testing,is there evidence that the population mean waiting time to check out is less than 11.02 minutes? What are the null and alternative hypotheses for this test?
Solution
The null hypothesis (H0) and alternative hypothesis (H1) for this test would be:
H0: μ = 11.02 (The population mean waiting time to check out is equal to 11.02 minutes) H1: μ < 11.02 (The population mean waiting time to check out is less than 11.02 minutes)
The test is a one-tailed t-test because we are testing if the population mean waiting time is less than 11.02 minutes.
Steps to perform the hypothesis test:
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Calculate the test statistic: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)) t = (9.79 - 11.02) / (5.6 / sqrt(50)) t = -1.23 / 0.79 t = -1.55
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Determine the critical value: The critical value for a one-tailed t-test at the 0.01 level of significance with 49 degrees of freedom (sample size - 1) can be found in the t-distribution table. The critical value is -2.405.
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Compare the test statistic with the critical value: Since the test statistic (-1.55) is greater than the critical value (-2.405), we do not reject the null hypothesis.
Conclusion: At the 0.01 level of significance, using the critical value approach to hypothesis testing, there is not enough evidence to conclude that the population mean waiting time to check out is less than 11.02 minutes.
Similar Questions
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