One of the major costs involved in planning a summer vacation is the cost of lod

Question

One of the major costs involved in planning a summer vacation is the cost of lodging. Even within a particular chain of hotels, costs 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 Marriott, Radisson, and Wyndham hotel chains, and record the nightly room rates. a) Find a 95% confidence interval for the difference in the average room rates for the MARRIOTT and the Wyndham hotel chain. b Find a 99% confidence interval for the difference in the average room rates for the Radisson and the Wyndham hotel chain. c) Do the intervals in parts a and b contain the value mu_1 - mu_2 = 0? Why is this of interest to the researcher? d) Do the data indicate a difference in the average room rates between the Marriott and the Wyndham chains?

Explanation / Answer

a) mean1 = 170 , mean2 = 150 , s1 = 17.5 , s2 = 16.5 , n = 50

At 95% confidence interval z value = 1.96

CI = (mean1 - mean2) + /- z * sqrt(s1^2/n1 + s2^2 / n2)

= ( 170 - 150) + /- 1.96 *( 17.5 / sqrt(50) + 16.5/ sqrt(50))

= (13.333, 26.667)

b)

mean1 = 145 , mean2 = 150 , s1 = 10 , s2 = 16.5 , n = 50

At 99% confidence interval z value = 2.576

CI = (mean1 - mean2) + /- z * sqrt(s1^2/(n) + s2^2 / (n))

= ( 145 - 150) + /- 2.576 *( 10 / sqrt(50) + 16.5/ sqrt(50))

= (12.971 , 27.028)

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