1) Conde Nast Traveler conducts an annual survey in which readers rate their favorite cruise. Cruises are rated on a 100 point scale, with higher values indicating better service. A sample of 37 cruise ships carrying fewer than 500 passengers resulted in an average rating of 85.36 and a sample of 44 cruise ships carrying 500 or more passengers received an average rating of 81.40 (Conde Nast Traveler, February 2008). Suppose the population standard deviation is 4.55 for cruise ships carrying fewer than 500 passengers and 3.97 for those carrying 500 or more.

a) What is the 95% confidence interval estimate for the difference between the population mean ratings of both cruise sizes?

b) Is the average rating for cruise ships carrying more than 500 passengers higher than for those carrying less than 500 passengers?

2) Consumer Reports magazine surveys its readers to find out customer satisfaction ratings for the nation's largest stores (Consumer Reports, March 2012). Each respondent is asked to rate specific stores in relation to six factors: product quality, selection, value, checkout efficiency, service, and store design. Overall customer satisfaction is summarized in a rating, where 100 means that the respondent is fully satisfied in relation to all six factors. The following are representative sample data from independent samples of Target and Walmart customers.

TargetWal-Mart

n₁ = 25n₂ = 30

= 79 = 71

a) Formulate the alternative and null hypotheses to test whether there are differences in the population mean of the customer satisfaction rating between the two stores. Assume that previous experience with Consumer Reports' satisfaction scale tells you that assuming a population standard deviation of 12 is reasonable for both stores. Perform the hypothesis test. What would your conclusion be at a significance level of 0.05?

b) Which of the two stores seems to have greater customer satisfaction, if one exceeds the other? Provide a 95% confidence interval for the difference in the population mean of the customer satisfaction ratings for both stores.

3) Safegate Foods Inc., is redesigning checkout boxes in its supermarkets across the country and testing two designs. Both systems were installed in two supermarkets and the time it took for customers to go through the checkout was measured. The results are summarized in the following table.

System ASystem B

n₁ = 120n₂ = 100

₁ = 4.1 min ₁ = 3.4 min

₁ = 2.2 min ₂ = 1.5 min

a) With 0.05 as the significance level, perform a hypothesis test to determine if the mean time for system A is at least the same as system B. Which system will be preferred?

b) Estimate the difference between the means with a 95% confidence coefficient

4) Financial services company Country Financial surveys adults 18 and older to determine if personal financial ability changes over time (USA Today, April 4, 2012). In February 2010, out of a sample of 900 adults, 315 claimed to have more than sufficient financial security.

a) Formulate the pertinent hypotheses in order to assess whether there are significant differences in the population proportions of the referred years. Use a significance level of 0.05. What are your conclusions?

b) What is the 95% confidence interval estimate of the difference between the two population proportions?

5) A large auto insurance company takes samples of insured men, married and single, and determines how many claimed the insurance in the previous three years.

Single policyholders Married policyholders

N1 = 400 n1 = 900

Amount used = 76 Amount used= 90

a) Use = 0.05. Take a test to determine if the claim ratio is different between married and single policyholders.

b) Provide a 95% confidence interval for the difference between the proportions of the two populations.