Arithmetic Mean and Five-step P-value Approach

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8. 17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8. 17 ounces. Suppose that in a particular of 50 packages, the mean amount dispensed is 8. 159 ounces, with a sample standard deviation of 0. 051 A. Is there evidence that the population mean amount is different from 8. 17 ounces? (Use a 0. 05 level of significance. ) B. Determine the p-value and interpret its meaning. 9. 27 In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SLBI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy complication stage in which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service. During a period of one month, a random sample of 27 approved policies is selected, and the total processing time, in days, is recorded (and stored in insurance): 73 19 16 28 31 56 45 17 22 18 91 92 50 51 69 A. In the past, the mean processing time was 45 days. At the 0. 05 level of significance, is there evidence that the mean processing time had changed from 45 days? B. What assumption about the population distribution is needed in order to conduct the t test in (a)? C. Construct a boxplot or a normal probability plot to evaluate the assumption made in (b). D. Do you think that the assumption needed in order to conduct the t test in (a) is valid? Explain. 93. 1 One operation of a steel mill is to cut pieces of steel into parts that are used in the same frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts must be cut within Ð’Â ± 0. 005 inch of the length specified by the automobile company. The file Steel contains a sample of 100 steel parts. The measurement reported is the difference, in inches, between the actual length of the teel part, as measured by a laser measurement device, and the specified length of the steel part. For example, a value of -0. 002 represents a steel part that is 0. 002 inch shorter than the specified length. A. At the 0. 05 level of significance, is there evidence that the mean difference is not equal to 0. 0 inches? B. Construct a 95% confidence interval estimate of the population mean, Interpret this interval. C. Compare the conclusions reached in (a) and (b). D. Because n= 100, do you have to be concerned about the normally assumption needed for the t test and t interval? 9. 45 In recent year, the Federal Communications Commission reported that the mean wait for repairs for ATT customers was 25. 3 hours. In an effort to improve this service, suppose that a new repair service process was developed. This new process, used for a sample of 100 repairs, resulted in a sample mean of 22. 3 hours and a sample standard deviation of 8. 3 hours. A. Is there evidence that the population mean amount is less than 25. 3 hours? (Use a 0. 05 level of significance. ) B. Determine the p- value and interpret its meaning. 9. 47 You are the manager ot a restaurant that delivers pizza to college dormitory rooms. You have Just changed your delivery process in an effort to reduce the mean time between the order and completion of delivery from the current 25 minutes. A sample mean of 22. 4 minutes and a sample standard deviation of 6 minutes. A. Using the six- step critical value approach, at the 0. 05 level of significance, is there evidence that the population mean delivery time value of 25 minutes? B. At the 0. 05 level of significance, use the five-step p-value approach? C. Interpret the meaning of the p- value in (b). D. Compare your conclusions in (a) and (b). 9. 53 The U. S. Department of Education reports that 46% of full-time college students are employed while attending college (data extracted from The Condition of Education 2009, National Center for Education Statistics, nces. ed. gov). A recent survey of 60 full-time students at Miami University found that 29 were employed. A. Use the five- step p-value approach to hypothesis testing and a 0. 05 level of significance to determine whether the proportion of full-time students at Miami University is different that the national norm of 0. 6. B. Assume that the study found that 36 of the 60 full-time students were employed and repeat (a). Are the conclusions the same? 9. 55 One of the issues facing organizations is increasing diversity throughout the organization. One of the ways to evaluate an organizations success at increasing diversity is to compare the percentage of employees in the organization in a particular position with a specific background to the percentage in a position with that specific background in the general workforce. Recently, a large academic medical center determined that 9 of 17 employees in a particular position were female, whereas 55% of the employees for this position in the general workforce were female. At the 0. 05 level of significance, is there evidence that the proportion of females in this position at this medical center is different from what would be expected in the general workforce? 9. 57 One of the biggest issues facing e-retailers is the ability to reduce the proportion of customers who cancel their transaction after they have selected their products. It has been estimated that about half of prospective customers cancel their transactions after they have selected their products (data extracted from B. Tedeschi, E- Commerce, a Cure for Abandoned Shopping Carts: A Web Checkout System That Eliminates the Need for Multiple Screens, The New York Times, February 14, 2005, p. C3). Suppose that a company changed its Web site so that customers could use a single page checkout process rather than multiple pages. A sample of 500 customers who had selected their products were provided with the new checkout system.