Business Quantitative
1. Automobile Insurance Premiums. The average annual premium for automobile insurance in the United States is $1,503. The following annual premiums ($) are representative of the web site’s findings for the state of Michigan.
1,905 3,112 2,312
2,725 2,545 2,981
2,677 2,525 2,627
2,600 2,370 2,857
2,962 2,545 2,675
2,184 2,529 2,115
2,332 2,442
Assume the population is approximately normal.
a. Provide a point estimate of the mean annual automobile insurance premium in Michigan.
b. Develop a 95% confidence interval for the mean annual automobile insurance premium in Michigan.
c. Does the 95% confidence interval for the annual automobile insurance premium in Michigan include the national average for the United States? What is your interpretation of the relationship between auto insurance premiums in Michigan and the national average?
2. Used Car Prices. According to the National Automobile Dealers Association, the mean price for used cars is $10,192. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether the population mean price for used cars at this particular dealership differed from the national mean. The prices for the sample of 50 cars are shown in the file UsedCars.
a. Formulate the hypotheses that can be used to determine whether a difference exists in the mean price for used cars at the dealership.
b. What is the p value?
c. At α=0.05, what is your conclusion?
