Income in Thousands 58 60 62 78 79 84 85 88 89 72 75 76 63 63 92 96 71 68 69 63 65 67 103 104 59 64 91 95 72 66 Number of Transactions 19 32 38 45 37 46 39 42 47 34 38 40 49 38 42 79 36 41 34 36 35 39 54 75 38 40 48 80 37 40 Unit 6 Exercise 1. Assume that data contained in the Numerical Data A.xls file is from a simple random sample of customers of a Canadian retailer. Use this data to answer the following: (4 Points) a. b. 2. 3. 4. Develop a point estimate of the mean number of transactions for the retailer. Develop a point estimate of the population standard deviation of the number of transactions. The average waiting time for customers at a fast food restaurant is 3.5 minutes. The population standard deviation is 2.2 minutes. (6 Points) a. Assume that the waiting time of customers at this restaurant follow a normal distribution, what is the probability that a simple random sample of 60 customers will have a sample waiting time of less than 3 minutes? b. Do we need to make any assumption on the distribution of waiting times for the calculation in Part a? Why or why not? c. What is the probability that a simple random sample of 120 customers will have a sample waiting time of less than 3 minutes? Traditionally, 30% of customers of a cell phone company leave after their term contract expires. If this is the true population proportion of churn (customers leaving after their term expired), answer the following questions: (6 Points) a. If simple random samples of 100 customers are taken from the population of customers of this company, describe the sampling distribution of the sample proportion of churn. b. What is the probability that a simple random sample of 100 customers will have a sample proportion of churn that is within 0.03 of the population proportion? c. Check the condition for using the normal distribution to approximate the sampling distribution of the sample proportion and see whether it is valid. A simple random sample of 120 items is taken from an inventory and the average unit cost on the items is $25. The population standard deviation is known to be $10.50. (8 Points) a. Construct a 95% confidence interval for the mean unit cost of the population b. 5. 6. What is the margin of error at the 90% confidence level? c. Construct a 95% confidence interval for the mean unit cost of the population if the sample unit cost is obtained from a random sample of 200 instead of 120. d. Based on the results from a. and c., what can you say about the effect of a larger sample size on the length of the confidence interval at the same confidence level? A simple random sample of 50 items is taken from an inventory and the average unit cost on the items is $24.5. The population standard deviation is not known. Instead the sample standard deviation s is also calculated from the sample and equals to $12.5. (4 Points) a. Construct a 99% confidence interval for the mean unit cost of the population b. What is the margin of error at the 95% confidence level? The average score on an employee satisfaction survey is found to be 3.7 (out of 5). The sample standard deviation is 1.25. These two statistics are calculated from a random sample of 30 employees in a mid-size professional firm. (4 Points) a. With 95% confidence, what is the margin of error? b. What is the 95% confidence interval estimate of the population mean score? 2. Annual starting salary for graduates of the BBA program in a Canadian University is expected to be between $45,000 and $65,000. A survey involving a random sample of graduates from this program is planned and the first order of business is to decide on an appropriate sample size. As usual, the 95% level of confidence will be used. (6 Points) a. What is the planning value for the population standard deviation to be used in the sample size formula for estimating the population mean starting salary? b. How large should the sample size be if the desired margin of error is $1200? c. How large should the sample size be if the desired margin of error is $ 800? b. The proportion of female customers in a recent satisfaction survey of 500 listeners for a Toronto radio station is found to be 0.52. (6 Points) a. b. Construct a 95% confidence interval for the population proportion of female listeners. What is the margin of error at the 90% level of confidence? c. If another survey in planned for the radio station and the estimate from this survey can be used as the planning value, calculate the required sample size if the desired margin of error is 4% at the 95% confidence level. c. 100 of a random sample of 800 Ontario drivers admitted that in the last month they have used a smart phone while driving. This random sample is considered representative of Ontario drivers. (4 Points) a. b. Construct a 95% confidence interval to estimate the proportion of Ontario drivers who used a smart phone while driving in the last month. What is the margin of error of the estimate at the 99% confidence level? d. In a survey, the planning value for the population proportion is p* = 0.35. How large should the sample size for the survey be if the desired level of confidence is 90% and the desired margin of error is 0.03? (2 Points)