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13th Edition

Anderson

Publisher: CENGAGE L

ISBN: 9781305881884

Chapter 10.1, Problem 4E

Textbook Problem

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*Condé Nast Traveler* conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100-point scale, with higher values indicating better service. A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of 85.36, and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40. Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry 500 or more passengers.

- a. What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
- b. At 95% confidence, what is the margin of error?
- c. What is a 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

**a.**

To determine

Find the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers.

**Calculation:**

A sample of 37 ships which carry fewer than 500 passengers have an average rating of 85.36 and a sample of 44 ships which carry 500 or more passengers have an average of 81.40. The population standard deviation for the ships that carry fewer than 500 passengers is 4.55 and the population standard deviation for the ships that carry 500 or more passengers is 3.97.

Here,

The point estimate of the difference between two population means is

**b.**

To determine

Find the margin of error at 95% confidence.

**c.**

To determine

Find the 95% confidence interval estimate of the difference between the mean ratingsfor two sizes of ships.

STATISTICS F/BUSINESS+ECONOMICS-TEXT

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