# Chapter 91. A random sample of 75 group leaders, supervisors, and similar personnel at General Motor

Chapter 91. A random sample of 75 group leaders, supervisors, and similar personnel at General Motors revealed that, on average, they spent 7.5 years on the job before being promoted. The standarddeviation of the sample was 1.7 years. Construct a 95 percent confidence interval.2.A recent survey of 48 executives who were laid off during a recent recession revealed it took amean of 28 weeks for them to find another position. The standard deviation of the sample was6.8 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonablethat the population mean is 28 weeks? Justify your answer.3. The Human Relations Department of Electronics Inc. would like to include a dental plan as partof the benefits package. The question is: How much does a typical employee and his or her familyspend per year on dental expenses? A sample of 48 employees reveals the mean amount spent lastyear was \$1900, with a standard deviation of \$700.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 hecould afford \$1,700 of dental expenses per employee. Is it possible that the population meancould be \$1,700? Justify your answer.Chapter 104. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tirecan be driven before the tread wears out is 65,000 miles. Assume the mileage wear follows thenormal distribution and the standard deviation of the distribution is 5,000 miles. Crosset TruckCompany bought 48 tires and found that the mean mileage for its trucks is 59,000 miles. IsCrossetâ€™s experience different from that claimed by the manufacturer at the .05 significance level?Apply 5-step process for hypothesis testing and make a decision.5. Transmission EX Company manufactures truck transmissions. The weekly production of theModel EX-25 follows a normal probability distribution with a mean of 250 and a standarddeviation of 22. Economic recovery and higher sales of trucks requires boost in output of theplant and therefore more advanced assembly machinery has been installed. The head ofmanufacturing would like to know if her ideas has paid off and the mean of daily production isdifferent from 250 at the .01 significance level? Follow the 5-step hypothesis testing and showyour decision.