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 85.33, and a sample of 43 ships that carry 500 or more passengers provided an average rating of 81.9. assume that the population standard deviation is 4.58 for ships that carry fewer than 500 passengers and 3.95 for ships that carry 500 or more passengers.

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 sizes of ships?

(a) 3.43

              (b)  1.89

              (c) 1.54 to 5.32

Step-by-step explanation:

(a)  Let represent the average ratings of ships that carry fewer than 500 passengers and represent the ship that carry more than 500 passengers. Then , the point of estimate of the difference between the population mean rating for the ships that carry fewer than 500 passengers and the population mean rating for ship that carry 500 or more passengers is given as : – , which is  

85.33 – 81. 9

= 3.43

(b) To find the margin error  using 95% Confidence Interval and  = 1.96

Since we are dealing with two samples , the formula is given as

–  ±

Where sigma is the standard deviation

We have, 3.43 ± 1.96

= 3.43 ± 1.96( 0.9643)

= 3.43 ± 1.89

Therefore the margin error is 1.89

(c) the 95% confidence interval estimate of the difference between the population mean ratings for the two sizes of ships implies

3.43 – 1.89 t0 3.43 + 1.89

= 1.54 to 5.32

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.