Question

You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.6 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.35 minutes, with a sample standard deviation of 0.9 minute. Complete parts (a) and (b) below. a. At the 0.10 level of significance, is there evidence that the population mean waiting time is different from 3.6 minutes? State the null and alternative hypotheses. Ho: HVO H1: (Type integers or decimals.) Determine the test statistic. The test statistic is . (Round to two decimal places as needed.) Find the p-value. p-value = (Round to three decimal places as needed.) State the conclusion. | Ho. There is evidence to conclude that the population mean waiting time is different from 3.6 minutes. b. Because the sample size is 81, do you need to be concerned about the shape of the population distribution when conducting the t test in (a)? Explain. Choose the correct answer below. OA. Yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. In general, the t test is only appropriate for a normally distributed sample. OB. Yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. In general, the t test requires a larger sample size. OC. No, because n is equal to 81, the sampling distribution of the t test is approximately normal. In general, the t test is appropriate for this sample size unless the population is skewed. OD. No, because n is equal to 81, the sampling distribution of the t test is approximately normal. In general, the t test is appropriate for a large sample size.

Answer 1

Given Population mean Given mean Standard deviation sample size = 3.6 = 3.35 = 0.9 n = 81 Test hypothesis are Null hypothesis Alternate hypothesis Ho: H:H = * 3.6 3.6 df Test statistic 0-1 = 80 Test statistic t=* = s/n = (3.35-3.6)/(0.9/81) -2.5 P-value P(|t>2.5) = 0.0145 (Two tailed) Decision Since p-Value <0.10 hence reject the Ho Reject Ho, there is suficient evidence to conclude that the proportion of waiting time is different from 3.6 minutes Option C is correct