Please show work

Even within a particular chain of hotels, lodging during the summer months can vary substantially depending on the type of room and the amenities offered. Suppose that we randomly select 50 billing statements from each of the computer databases of the Hotel A, the Hotel B, and the Hotel C chains, and record the nightly room rates. The means and standard deviations for 50 billing statements from each of the computer databases of each of the three hotel chains are given in the table.

Hotel A Hotel B Hotel C

Sample Average ($) 155 175 110

Sample Standard Deviation       17.4   22.3   12.3

a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Round your answers to two decimal places.)

$ ____ to $ _____

(b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Round your answers to two decimal places.)

$_____ to $_____