The average cost per night of a hotel room in New York City is $266 ( SmartMoney

Question

The average cost per night of a hotel room in New York City is $266 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $70

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.

Explanation / Answer

mean = 266

n = 45

std dev = 70

z = 1.96

margin of error = 1.96 * 70/sqrt(45) = $20

95% C.I.

[266 - 1.96*70/sqrt(45) , 266 + 1.96*70/sqrt(45)]

(246,286)

(266-229)/70 = 0.52

The increase in two years has been by 0.52 std dev

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