BUSINESS STATISTICS-2

1. As part of a safety check, the Pennsylvania Highway Patrol randomly stopped 25 cars and checked their tire pressure. The sample mean was 32 pounds per square inch with a sample standard deviation of 2 pounds per square inch. Develop a 98 percent confidence interval for the population mean. 2. A human resource manager for Carver County is evaluating a recent effort to improve the health of the county’s firefighters by providing an exercise room in each of the county’s firehouses. Their records prior to installing the exercise rooms indicate that the mean weight of all county firefighters is 198 pounds with a standard deviation of 13 pounds. A random sample of 40 firefighters taken six months after the program was implemented revealed that the mean of the sample was 192 pounds. Construct a 96% confidence interval for the mean weight of all firefighters six months after the exercise rooms were installed. Assume that σ has not changed. Does it appear that the program is working? 3. The Department of Economic and Community Development (DECD) reported that in 2009 the average number of new jobs created per county was 450. The department also provided the following information regarding a sample of 5 counties in 2010. County New Jobs Created In 2010 Bradley 410 Rhea 480 Marion 407 Grundy 428 Sequatchie 400 a. Compute the sample average and the standard deviation for 2010. b. We want to determine whether there has been a significant decrease in the average number of jobs created. Provide the null and the alternative hypotheses. c. Use the testing of hypothesis for your conclusion. 4. A producer of various kinds of batteries has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours. a. Give the null and the alternative hypotheses. b. Compute the test statistic. c. At 99% confidence using the critical value approach, test management's belief. d. What is your conclusion based on testing of hypothesis?