The average cost per night of a hotel room in New York City is $278 ( SmartMoney

Question

The average cost per night of a hotel room in New York City is $278 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.

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.
to

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.

Explanation / Answer

Solution:-

a. 95% confidence interval for Z= 1.96 (check standard normal table)

Formula: margin of error= Z*s/vn

= 1.96*65/sqrt(45)

= 18.9916

= 19

b) The 95% confidence interval: xbar ± Z*s/vn

= 278 ± 1.96*65/sqrt(45)

= (259, 297)

c. does not change of cost

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