1. 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 standard deviation 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 a mean of 28 weeks for them to find another position. The standard deviation of the sample was 6.8 weeks. Construct a 95 percent confidence interval for the population mean. Is it reasonable that 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 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 48 employees reveals the mean amount spent last year 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 he could afford $1,700 of dental expenses per employee. Is it possible that the population mean could be $1,700? Justify your answer.
4. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 65,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,000 miles. Is Crosset’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 the Model EX-25 follows a normal probability distribution with a mean of 250 and a standard deviation of 22. Economic recovery and higher sales of trucks requires boost in output of the plant and therefore more advanced assembly machinery has been installed. The head of manufacturing would like to know if her ideas has paid off and the mean of daily production is different from 250 at the .01 significance level? Follow the 5-step hypothesis testing and show your decision.