A travel magazine conducts an annual survey where readers rate their favorite cr

Question

A travel magazine conducts an annual survey where readers rate their favorite cruise ship. Ships are rated on a 10 point scale, with higher values indicating better service. A sample of 30 ships that carry fewer than 500 passengers resulted in a average rating of 8.13 with standard deviation 0.57. A sample of 35 ships that carry more than 500 passengers resulted in an average rating of 8.38 with standard deviation 0.79. 

Give a 98% confidence interval of the difference between the population mean ratings for smaller ships and the population mean ratings for larger ships. (Note, the order of subtraction matters...look at the wording carefully.)

 _____±  _______Rounded to 2 decimal places.

Explanation / Answer

Ans:

Assumed unequal population variances.

df=30-1=29

critical t value=tinv(0.02,29)=2.462

98% confidence interval for difference between means

=(8.13-8.38)+/-2.462*sqrt((0.57^2/30)+(0.79^2/35))

=-0.25+/-0.42

=(-0.67, 0.17)

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