Question

The average cost per night of a hotel room in New York City is $275 (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?

b. What is the 95% confidence interval estimate of the population mean?

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. a)cannot conclude price has changed b)can conclude price has risen c)can conclude price has fallen

Answer 1

a) At 95% confidence interval the critical value is t^* = 2.015

Margin of error = t^* * s/

= 2.015 * 70/

= 21.0265
b) The 95% confidence interval is

+/- ME

= 275 +/- 21.0265

= 253.9735, 296.0265

c) Since the interval does not contain 229 and the lower limit is greater than 229, so we can conclude that the price has risen.

Option - B is correct.