Question

Hotel_Brand_1_Stay_Length   Hotel_Brand_2_Stay_Length
4   5
2   1
2   1
1   5
2   9
5   5
4   6
3   4
8   6
1   4
2   3
1   5
2   8
1   3
4   3
2   1
2   9
2   4
1   4
4   2
6   5
1   2
2   2
2   3
3   1
10   1
5   2
4   4
7   3
4   8
2   5
7   5
2   8
2   5
7   4
5   4
1   2
5   3
1   3
5   13
6   2
5   12
3   2
3   2
1   1
3   1
2   4
5   10
4   1
2   5
1   5
6   2
6   2
4   10
3   2
3   2
1   3
3   4
1   8
2   2
3   8
2   3
1   1
1   3
1   3
3   4
1   5
1   2
3   4
3   7
5   2
5   2
5   4
4   3
2   5
2   3
6   3
8   5
2   4
9   2
4   6
1   8
3   7
8   5
4   5
3   1
5   10
1   1
2   6
3   1
8   5
4   3
4   1
4   5
5   6
1   2
5   3
2   5
8   6
3   3

A hotel chain wants to determine whether there is a difference in the length of stays at two of its different brands of hotels. A simple random sample of 100 stay lengths was taken for each hotel brand. These data are shown below. Assume that the variances are not equal. a) State the appropriate null and alternative hypotheses. b) Based on these sample data and a 0.10 level of significance, what conclusion should be made about the average length of stay at these two hotel chains? Click the icon for sample data on the length of stays at these hotel chains. a) State the appropriate null and alternative hypotheses. Let Hy be the population mean length of stay at hotel brand 1, and let hy be the population mean length of stay at hotel brand 2. O A. Ho H, H270 HA: H1-H2 = 0 C. Ho H, -H2<0 HAH-H220 OB. Ho H, H2 = 0 HAM-H20 OD. HOH-H250 HAH-420 b) Calculate the value of the test statistic. The test statistic is (Round to two decimal places as needed.) Calculate the p-value. The p-value is (Round to four decimal places as needed.) State the appropriate conclusion for the hypothesis test. O A. Reject Ho. There is sufficient evidence at the a=0.10 level of significance to conclude that the hotel brands have different average stay lengths. Click to select your answer(s). Save for Later

Answer 1

The statistical software output for this problem is:

Two sample T hypothesis test: V1 : Mean of Hotel_Brand_1_Stay_Length 12 : Mean of Hotel_Brand_2_Stay_Length V1 - H2 : Difference between two means Ho : 11 - 12 = 0 HA: P1 - H270 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. DF T-Stat H1 - H2 -0.7 0.33572175 191.1768 -2.08506 P-value 0.0384

Hence,

Hypotheses: Option B is correct.

Test statistic = -2.09

P - value = 0.0384

Conclusion: Option A is correct.