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.

1. What is the p-value of the hypothesis test. Round your answer to 4 decimal places.

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

3. What are the null and alternative hypotheses to test whether there is a difference between the population proportions for the two years?

options:

H₀: p₁ - p₂  0 and H_a: p₁ - p₂ > 0 ;

H₀: p₁ - p₂ = 0 and H_a: p₁ - p₂  0 ;

H₀: p₁ - p₂  0 and H_a: p₁ - p₂ < 0 ;

H₀: p₁ - p₂ = 0 and H_a: p₁ - p₂ > 0

4. At a α = 0.01, what is your conclusion?

options:

Do not reject H0, since p-value < .01 ;

Reject H0, since p-value > .01 ;

Reject H0, since p-value < .01 ;

Do not reject H0, since p-value > .01

Answer 1

let sample 1 is meant for ships carrying less than 500 passengers

sample 2 is meant for ships carrying 500 or more passengers

for sample 1 we have

sample size =n1=37

sample mean =m1=85.36

population SD=SD1=4.55

for sample 2 we have

sample size=n2=44

sample mean =m2=81.40

population SD=SD2=3.97

we have to test that if mean difference is ZERO or not

so

now test statistics is given by

test is two tailed so

P-Value =2*P(Z>4.13) =2*0.000001 =0.000002

since P value is less than level of significance hence we reject H0