Hypothesis Testing and Estimating Single Population Parameters

8.76

A random sample of 25 SUV's of the same year and model revealed the following miles per gallon (mpg) values:

12.4 13.0 12.6 13.1

13.0 12.0 13.1 12.6
9.5 13.25 12.4 11.7
10.0 14.0 10.9 10.2
11.0 11.9 9.9 11.3

Assume the population for this model year is normally distributed.

A. Use the sample results to develop a 95% confidence interval estimate for the population mean miles per gallon.
B. Determine the average number of gallons of gasoline the SUV's described here would use to travel between Los Angels and San Francisco California-a distance of approximately 400 miles.
C. Another sample of the same size is to be obtained. If you know that the average miles per gallon in the second sample will be larger than the one obtained in part A, determine the probability that the sample mean will be larger than the upper confidence limit of the confidence interval you calculated.

9.48

You are given the following information null and alternative hypotheses:

Ho: µ < 500
HA: µ > 500
&#945; = 0.01

Calculate the probability of committing a Type II error when the population mean is 505, the sample size is 64, and the population standard deviation is known to be 36.

9.98

MBNA offers personal and business credit cards, loans, and savings products. It was bought by Bank of America in June 2005. One of the selling points for MBNA was its position relative to the rest of the credit card industry. MBNA's customers' average annual spending per active account before its purchase was $6,920. To demonstrate its relative position in the industry, MBNA's CFO, H Vernon Wright, might authorize a survey producing the following data on the annual spending, to the nearest dollar, of accounts in the industry;

3680 6255 6777 7412 4902 5522 5190 7976 4116 3949
6814 2264 4991 5353 5914 5828 6059 6354 6193 5648
6117 7315 6458 4973 6554 1926 4395 5341 4921 6248
4061 4777 5876 5984 3381 5441 4268 7657 6449 4821

A. Conduct a hypothesis test to determine if MBNA has a larger average annual spending per active account than the rest of the credit card industry. Use a p-value approach and significance level of 0.025.
B. If the industry's annual spending per active account was normally $5,560 and the standard deviation of $1140, determine the probability that a randomly chosen account would have an annual spending larger than MBNA's.