Question

The average cost per night of a hotel room in New York City is $263 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $50.

a. With 95% confidence, what is the margin of error? Round your answer to the nearest dollar.

b. What is the 95% confidence interval estimate of the population mean? Round your answers to the nearest dollar.

c. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period. PICK FROM FOLLOWING

price has fallen, price has not change or price has increased

Answer 1

Solution:-

a) The margin of error is 14.609.

b) 95% confidence interval estimate of the population mean C.I = (248.39, 277.609).

$C.I = \bar{x}\pm z_{\alpha /2}\ast \frac{\sigma }{\sqrt{n}}$

C.I = 263 + 1.96*7.4536

C.I = 263 + 14.609

C.I = (248.39, 277.609)

c) Since all the points in the confidence interval are greater than 229, hence we can conclude that price has increased over the two-year period.