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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 ($) 140 160 110 Sample Standard 17.8 22.5 Deviation 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. (Use Hotel A - Hotel B. 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. (Use Hotel B - Hotel C. Round your 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 - M2) = 0. Yes, the interval in part (b) contains (#1 - #2) = 0. Yes, both intervals contain (#1 - #2) = 0. O No, neither interval contains (#1 - #2) = 0. Why is this of interest to the researcher? O If (H1 - M2) = 0 is contained in the confidence interval, it is implied that the average room rate for the two hotels was $0. O If (#1 - 12) = 0 is contained in the confidence interval, it is implied that there is a difference in the average room rates for the two hotels. If (H1 - M2) = 0 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. O If (H1 - M2) = 0 is contained in the confidence interval, it is implied that the room rate for one of the hotels was $0. O If (H] - M2) = 0 is contained in the confidence interval, it is implied that there was an error in the database records. (d) Do the data indicate a difference in the average room rates between the Hotel A and the Hotel B chains