An online travel agent that specializes in cruises wanted to compare the cost of

Question

An online travel agent that specializes in cruises wanted to compare the cost of cruising to different destinations on various cruise lines. The following random sample data show the average cost of a seven-day cruise in a standard room to two locations. Assume the population variances for the cruise fares for these destinations are equal. Complete parts a through c. Location 1 Location 2 Sample mean S985 $926 Sample standard deviation S131 5128 Sample size 9 a. Construct a 90% confidence interval to estimate the difference between the average rates of cruising to location 1 vs. cruising to location 2. The 90% confidence interval is (DD) (Round to two decimal places as needed.) b. What conclusions can be made about the difference in rates between these destinations? with 90% confidence, it can be said that the difference in rates between these destinations V the endpoints of the confidence interval. The fact that this interval v zero provides evidence that there a significant difference between these two rates. c. What assumptions need to be made in order to perform this procedure? O A. If both sample sizes are not each at least 30, then one must assume that the underlying populations are normally distributed to perform this procedure. Also, one must assume that the samples are independent. OB. Although the sample size in the second sample is large enough, it must be assumed that the distribution for the first sample is normally distributed. OC. Although the sample size in the first sample is large enough, it must be assumed that the distribution for the second sample is normally distributed OD. Since the sample sizes are large enough, no assumptions are needed.

Explanation / Answer

solution:- Given information
Location 1 Location 2
sample mean $985 $926
sample sd $131 $128
sample size 9 11

a) 90% confidence interval : df = 9+11-2 = 18 , t = 1.734

= (X1 - X2) +/- t*sqrt[s1^2/n1 +s2^2/n2]
= (985 - 926)+/- 1.734*sqrt[(131^2/9) + (128^2/11)]
= ( -42.0527 , 160.0527)

b) with 90% confidence,it can be said that the difference in rates between these destinations
falls within the endpoints of the confidence interval.the fact that this interval includes Zero provides evidence that there is not a significant difference between the two rates.

c) option A.

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