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 the data are given in the table. Hotel A Hotel B Hotel C Sample Average ($) 140 165 120 Sample Standard 17 2 22 4 12 9 Deviation ' ' ' (a) Find a 95% confidence interval for the difference in the average room rates for the Hotel A and the Hotel B chains. (Use Hotel A Hotel B. Round your answers to two decimal places.) $l:lt$i:i (b) Find a 99% confidence interval for the difference in the average room rates for the Hotel B and the Hotel C chains. (Use Hotel B Hotel C. Round your answers to two decimal places.) $l:lt$S (c) Do the intervals in parts (a) and (b) contain the value ([41 [42) = 0? 0 Yes, the interval in part (a) contains (\"1 #2) = O. 0 Yes, the interval in part (b) contains (\"1 #2) = 0. 0 Yes, both intervals contain (#1 \"2) = O. O No, neither interval contains (#1 '42) = 0. Why is this of interest to the researcher? Q If (#1 \"2) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0. 0 If (#1 \"2) = 0 is contained in the confidence interval, it is implied that there was an error in the database records. 0 If (#1 \"2) = O is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0. 0 If (#1 \"2) = O is contained in the confidence interval, it is implied that we cannot conclude there is a difference in the average room rates for the two hotels. 0 If (#1 \"2) = O is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels. (d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel B chains? O Yes, the data indicate a difference in the average room rates between the Hotel A and the Hotel B chains. O No, the data do not indicate a difference in the average room rates between the Hotel A and the Hotel B chains. Do the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains? O Yes, the data indicate a difference in the average room rates between the Hotel B and the Hotel C chains. O No, the data do not indicate a difference in the average room rates between the Hotel B and the Hotel C chains