You run a fast-food restaurant and you are assessing the speed of service at your drive through window. If the volume is fewer than 50 cars served per hour you will need to allocate more staff to the drive through window. You record the number of cars served for each of 30 random hours for a sample size of 30. The sample average cars served per hour is x = 46 and the sample standard deviation is s = 12. a. Test whether the population mean for cars served per day is less than 50 with a 1% significance level. The z-critical value for this test is ???? = ??0.01 = 2.33. Show all your steps clearly and illustrate your answer with a graph. b. Explain what is meant by the term “statistically significant.” Is the result you obtained in part a statistically significant? c. Describe what happens to the magnitude of the Z-statistic (with reference to the Z-statistic formula) when the following occurs. For each, explain intuitively the effect on the statistical significance of the test result. i. The sample size increases. ii. The value of ?? moves closer to μ0.
You run a fast-food restaurant and you are assessing the speed of service at your drive through window. If
the volume is fewer than 50 cars served per hour you will need to allocate more staff to the drive through
window. You record the number of cars served for each of 30 random hours for a
sample average cars served per hour is x = 46 and the sample standard deviation is s = 12.
a. Test whether the population mean for cars served per day is less than 50 with a 1% significance level. The
z-critical value for this test is ???? = ??0.01 = 2.33. Show all your steps clearly and illustrate your answer with
a graph.
b. Explain what is meant by the term “statistically significant.” Is the result you obtained in part a
statistically significant?
c. Describe what happens to the magnitude of the Z-statistic (with reference to the Z-statistic formula) when
the following occurs. For each, explain intuitively the effect on the statistical significance of the test result.
i. The sample size increases.
ii. The value of ?? moves closer to μ0.
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