Urban Plastic Products, Inc. is concerned about the inside diameter of the plastic PVC pipe it produces. A machine extrudes the pipe, which is then cut into 10-foot lengths. About 720 pipes are produced per machine during a two-hour period. How would you go about taking a sample from the two-hour production period?
A state meat inspector in Iowa has been given the assignment of estimating the mean net weight of packages of ground chuck labeled “3 pounds.” Of course, he realizes that the weights cannot be precisely 3 pounds. A sample of 36 packages reveals the mean weight to be 3.01 pounds, with a standard deviation of 0.03 pounds.
a. What is the estimated population mean?
b. Determine a 95 percent confidence interval for the population mean.
The Human Relations Department of Electronics, Inc., would like to include a dental plan as part of the benefits package. The question is: How much does a typical employee and his or her family spend per year on dental expenses? A sample of 45 employees reveals the mean amount spent last year was $1,820, with a standard deviation of $660.
a. Construct a 95 percent confidence interval for the population mean.
b. The information from part (a) was given to the president of Electronics, Inc. He indicated he could afford $1,700 of dental expenses per employee. Is it possible that the population mean could be $1,700? Justify your answer.
Dole Pineapple, Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces, with a sample standard deviation of 0.03 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.
The owners of the Franklin Park Mall wished to study customer shopping habits. From earlier studies the owners are under the impression that a typical shopper spends 0.75 hours at the mall, with a standard deviation of 0.10 hours. Recently the mall owners added some specialty restaurants designed to keep shoppers in the mall longer. The consulting firm, Brunner and Swanson Marketing Enterprises, has been hired to evaluate the effects of the restaurants. A sample of 45 shoppers by Brunner and Swanson revealed that the mean time spent in the mall had increased to 0.80 hours.
a. Develop a test of hypothesis to determine if the mean time spent in the mall is more than
0.75 hours. Use the .05 significance level.
b. Suppose the mean shopping time actually increased from 0.75 hours to 0.77 hours. What is the probability this increase would not be detected?
c. When Brunner and Swanson reported the information in part (b) to the mall owners, the owners were upset with the statement that a survey could not detect a change from 0.75 to 0.77 hours of shopping time. How could this probability be reduced?