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 ships that carry fewer than 500 passengers and a sample of ships that carry 500 or more passengers is provided in the Microsoft Excel Online file below (Condé Nast Traveler, February 2008).

Round your all answers to two decimal places.

10.1 Microsoft Excel: Structured Activity Question 1 010 Video Excel Online Structured Activity: Inferences About the Difference Between Two Population Means, σ1 and σ2 Known 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 ships that carry fewer than 500 passengers and a sample of ships that carry 500 or more passengers is provided in the Microsoft Excel Online file below (Condé Nast Traveler, February 2008) Round your all answers to two decimal places. 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 szes of ships? to Check My Work Reset Problem

Answer 1

SAMPLE SIZE 1= 37

SAMPLE SIZE 2 =44

SAMPLE 1 MEAN= (SUM OF VALUES OF SAMPLE 1) / 37

=3046.24/37=82.33

SAMPLE 2 MEAN =(SUM OF VALUES OF SAMPLE 2) / 44

=3598.94/44=81.79

MEAN DIFFERENCE= SAMPLE 1 MEAN- SAMPLE 2 MEAN

= 82.33-81.79= 0.54

SAMPLE 1 STANDARD DEVIATION=5.628703

SAMPLE 1 VARIANCE= STANDARD DEVIATION² =31.68

SAMPLE 2 STANDARD DEVIATION=5.052322

SAMPLE 2 VARIANCE=25.53

STANDARD ERROR= STANDARD DEVIATION/ SAMPLE SIZE^1/2

STANDARD ERROR SAMPLE 1= 5.628703/37^1/2= 0.93

STANDARD ERROR SAMPLE 2= 5.052322/44^1/2= 0.76

Z CRITICAL VALUE FOR A TWO TAILED AT 95% CI= 1.96

MARGIN OF ERROR = CRITICAL VALUE * STANDARD ERROR

MARGIN OF ERROR SAMPLE 1= 1.96*0.93=1.82

MARGIN OF ERROR SAMPLE 2=1.96*0.76= 1.49

TO CALCULATE LIMITS AT 95% CI WE USE -1.96<X-$\mu$/$\sigma$<1.96

SAMPLE 1- LOWER LIMIT= 71.23 UPPER LIMIT= 93.36

SAMPLE 2 LOWER LIMIT= 71.89 UPPER LIMIT= 91.69