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Problem 1 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 1 = 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 za = 20.01 = 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 x moves closer to mo.
Problem 2 Calculate the following using the provided normal probability table. Illustrate your answers with graphs. a. P(-1.2 <Z 1.3) = ? b. P(X > 10) =? where X is distributed normal with u = 9 and 6 = 4. c. The 79th percentile of X, where X is distributed normal with u = 5 and o=16. d. P(41 S X < 44) = ?, where X is calculated from random sample of n = 81 selected from a normally distributed population, X-N(40, 144).
Eco Mg1230_322_midterm2_1010.docx- 2 of 2 Problem 3 You run a call center and you need to determine the typical length of a technical support call to your center. The research department takes a random sample of 60 calls and calculates the sample average length of a call ž to be 15 minutes and the sample standard deviations to be 7 minutes. a. Calculate the 99% confidence interval for u, the population mean time for length of a technical support call. The Z-critical value for this interval is za = 2001 = 20.005 = 2.575. b. Interpret the confidence interval in words. c. The vice president of research asserts that the mean length of a call is 10 minutes. Do you agree with this? Explain how you know. d. Suppose your company needs a narrower confidence interval, so it can decide whether more training is necessary for its technical support staff. Calculate the sample size necessary to estimate the population mean within 1 minute.
Problem 4 In a test of the hypothesis Ho: d = 50 versus HA: > 50 a sample of n = 40 observations was found to have mean x = 58 and standard deviation s = 25. a. Give the definition of a p-value. b. Calculate the p-value for this test. c. Can you reject the null hypothesis at the 10% level of significance? at the 5% level of significance? at the 1% level of significance? Explain the criterion you use. Illustrate your answer with a graph.