Even within a particular chain of hotels, lodging during thesummer months can vary substantially depending on the type of roomand the amenities offered. Suppose that we randomly select 50billing statements from each of the computer databases of the HotelA, the Hotel B, and the Hotel C chains, and record the nightly roomrates. The means and standard deviations for 50 billing statementsfrom each of the computer databases of each of the three hotelchains are given in the table.
| | Hotel A | Hotel B | Hotel C |
| Sample average ($) | 135 | 160 | 105 |
| Sample standarddeviation | 17.2 | 22.2 | 12.1 |
(a) Find a 95% confidence interval for the difference in theaverage room rates for the Hotel A and the Hotel C chains. (Roundyour answers to two decimal places.)
$ to $
(b) Find a 99% confidence interval for the difference in theaverage room rates for the Hotel B and the Hotel C chains. (Roundyour answers to two decimal places.)
$ to $
(c) Do the intervals in parts (a) and (b) contain the value(?1 ? ?2) = 0?
Yes, the interval in part (a) contains (?1 ??2) = 0.Yes, the interval in part (b) contains(?1 ? ?2) =0. Yes, both intervals contain(?1 ? ?2) = 0.No, neitherinterval contains (?1 ? ?2)= 0.
Why is this of interest to the researcher?
If (?1 ? ?2) = 0 iscontained in the confidence interval, it is implied that the roomrate for one of the hotels was $0.If (?1 ??2) = 0 is contained in the confidenceinterval, it is implied that there is no difference in the averageroom rates for the two hotels. If(?1 ? ?2) = 0 is containedin the confidence interval, it is implied that there was an errorin the database records.If (?1 ??2) = 0 is contained in the confidenceinterval, it is implied that there is a difference in the averageroom rates for the two hotels.If (?1 ??2) = 0 is contained in the confidenceinterval, it is implied that the average room rate for the twohotels was $0.
(d) Do the data indicate a difference in the average room ratesbetween the Hotel A and the Hotel C chains?
Yes, the data indicate a difference in the average room ratesbetween the Hotel A and the Hotel C chains.No, the data do notindicate a difference in the average room rates between the Hotel Aand the Hotel C chains.
Do the data indicate a difference in the average room rates betweenthe Hotel B and the Hotel C chains?
Yes, the data indicate a difference in the average room ratesbetween the Hotel B and the Hotel C chains.No, the data do notindicate a difference in the average room rates between the Hotel Band the Hotel C chains.
