The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65.

Question

a. With 95% confidence, what is the margin of error (to 2 decimals)?

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

Answer 1

a) a = 0.05 = z(0.025) = 1.96
Mean of error = Za/2* σ/√n
= 1.96 *65/√45
= 18.99
b) xbar-+ Za/2*σ/√n
= 273 -18.992, 273+ 18.992
= [254.008, 291.992]

Answer 2

Hello,
Thanks for your help the answers you got are the same as mine but the website where I do my homework says it is wrong.
Can you help me out please?

Answer 3

ta/2 = a = 0.05 = 0.025

t = 2.02
a. 19.57

b. (253.47, 292.53)