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Constructing a confidence interval to test a claim about the... A chain of taco restaurants claims that the population mean of the wait times in their drive-thru for all customers is 4.39 minutes. You work for a competitor and you want to test that claim. To do so, you select a random sample of 40 of the chain's drive-thru customers and record the wait time in the drive-thru for each. Assume it is known that the population standard deviation of the wait times in the drive-thru for the taco chain's restaurants is 2.79 minutes. Based on your sample, follow the steps below to construct a 90% confidence interval for the population mean of the wait times in the drive- thru for all customers. Then state whether the confidence interval you construct contradicts the restaurant chain's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 40 customers. Sample standard Population standard Number of customers Sample mean deviation deviation Take Sample 2.79 Enter the values of the sample size, the point estimate for the population mean, the population standard deviation, and the critical value you need for your 90% confidence interval. (Choose the correct critical value from the table of critical values provided.) When you are done, select "Compute". Sample size: X 5 ? 0 Standard error: Point estimate: Critical values Population standard deviation: Margin of error: Zo.005 = 2.576 Zo.010 = 2.326 Critical value: 0 Z0.025 = 1.960 90% confidence interval: Z 0.050 = 1.645 Compute Zo.100 = 1.282 (b) Based on your sample, graph the 90% confidence interval for the population mean of the wait times in the drive-thru for all customers. . Enter the lower and upper limits on the graph to show your confidence interval. . For the point (), enter the restaurant chain's claim of 4.39 minutes. 90% confidence interval: 0.00 10.00 5.00 0 N 8 10 X 5 ? (c) Does the 90% confidence interval you constructed contradict the restaurant chain's claim? Choose the best answer from the choices below. No, the confidence interval does not contradict the claim. The restaurant chain's claim of 4.39 X ? minutes is inside the 90% confidence interval. No, the confidence interval does not contradict the claim. The restaurant chain's claim of 4.39 minutes is outside the 90% confidence interval. Yes, the confidence interval contradicts the claim. The restaurant chain's claim of 4.39 minutes is inside the 90% confidence interval. Yes, the confidence interval contradicts the claim. The restaurant chain's claim of 4.39 minutes is outside the 90% confidence interval
