A major city in the United States has a large number of hotels. During peak trav

Question

A major city in the United States has a large number of hotels. During peak travel times throughout the year, these hotels use a higher price for their rooms. A travel agent is interested in finding the difference of the average cost of a hotel rooms from the peak season to the off season. He takes a random sample of hotel room costs during each of these seasons. Plots of both samples of data indicate that the assumption of

normality is not unreasonable.

Season Cost Standard Deviation Sample Size

Peak Season $245 $45 33

Off Season $135 $65 38

(a) Construct a 95 percent confidence interval for the difference of the mean cost of hotel rooms from peak season to the off season.

(b) One particular hotel has an off season rate of $88 and a peak season rate of $218.

Based on your confidence interval, comment on the price difference of this hotel.

Explanation / Answer

1 - 2 = (M1 - M2) = 110, 95% CI [105.48, 114.52].

Calculation

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 6250 / 69 = 90.58

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((90.58/33) + (90.58/38)) = 2.26

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 110 ± (1.99 * 2.26) = 110 ± 4.52

b) price diffrence = 218-88 = $130

It is outside the confidence interval of 95% and represents type 1 error

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