The waiting time to check out of a supermarket has had a population mean of 8.49 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 90 customers was selected,and their mean waiting time to check out was 7.85 minutes with a sample standard deviation of 4.9 minutes.Complete parts(a)through(d) H0:μ≥8.49 H1:μ<8.49 What is the test statistic for this test? -1.2391 (Round to four decimal places as needed.) What is the critical value for this test?
Question
The waiting time to check out of a supermarket has had a population mean of 8.49 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 90 customers was selected,and their mean waiting time to check out was 7.85 minutes with a sample standard deviation of 4.9 minutes.Complete parts(a)through(d) H0:μ≥8.49 H1:μ<8.49 What is the test statistic for this test? -1.2391 (Round to four decimal places as needed.) What is the critical value for this test?
Solution
The critical value for this test can be found using the Z-table for the standard normal distribution. Since this is a one-tailed test (H1: μ < 8.49), we look for the critical value that corresponds to the significance level of the test. If the significance level (alpha) is not given, it is typically assumed to be 0.05 for a one-tailed test.
To find the critical value (also known as the z-score), you would look up the value in the Z-table that corresponds to the remaining area in the tail. For a significance level of 0.05 in a one-tailed test, you would look up the value that corresponds to an area of 0.05 in the tail, which is -1.645.
So, the critical value for this test is -1.645. If the test statistic of -1.2391 is less than the critical value of -1.645, we would reject the null hypothesis. However, in this case, -1.2391 is greater than -1.645, so we would not reject the null hypothesis. This means that the supermarket's new system has not significantly reduced the waiting time to check out.
Similar Questions
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