Question

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.

What is the value of the test statistic ( z-value of p ¯ 1- p ¯ 2). Round to 4 decimal places.

Answer 1

Solution:

Given that,

= 85.36

= 81.40

= 4.55

= 3.97

n1 = 37

n2 = 44

The test statistic

z = ( - ) / ( / n1) + ( / n2 )

= (85.36 - 81.40) / ( 4.552/37) + ( 3.972 / 44)

= 4.1830

The value of the test statistic is 4.1830.