Question

Cruise ships have been in the news of late due to the concerns that they play in transporting COVID-19 to do different spots around the world. Prior to the outbreak a survey was done to rate the service occurring on cruise ships with the higher they scored on a 100-point scale representing the higher quality of service. The data showed that 27 ships carrying less than 500 passengers provided an average value of 85.36 and a population standard deviation of 4.55. For ships carrying more than 500 passengers showed that 44 ships provided an average value of 81.40 and a population standard deviation of 3.97.

* What is the point estimate of the difference between the population mean rating for ships carrying few than 500 and more than 500 passengers?

* At a 95% confidence level, what is the margin of error?

* What is the 95% confidence interval estimate of the difference between the population mean rating for the two sizes of ship?

Answer 1

Let denote the population mean rating for ships carrying few than 500 and more than 500 passengers.

The point estimate of the difference between the population mean rating for ships carrying few than 500 and more than 500 passengers is =  

ii) and iii)