Question

A travel association reported the domestic airfare (in dollars) for business travel for the current year and the previous year. Below is a sample of 12 nights with their domestic affares shown for both years. Current Previous 345 216 206 275 635 710 650 545 547 496 (a) Formulate the hypotheses and test for a significant increase in the mean domesticare for business travel for the one-year period. HolMa20 Ho No HOM* Ho: Puso OH. e s for Round your answer to the dom Calculate the test statistic (Use current year airfare - previous year 2.02 Calculate the p-value. ( Round your answer to four decimal places)

Answer 1

Solution: The data provided in the question statement can be tabulated as below. Calculating a few additional columns: (d - d)2 Current Year X1 345 526 420 Previous Year X2 315 475 474 206 275 432 Difference d = X1-X2 30 51 -54 | 64 841 5776 216 10 144 144 285 405 10 -27 2401 635 585 50 710 605 517 570 610 {x1 = 5844 650 545 547 496 580 x2 = 5580 60 60 -30 74 784 1444 1444 2704 2704 64 . (d - d) 2 = 18514 30 L d = 264 d = £d / n = 264/12 = 22 sa = /£ (d – d)/(n − 1) = 18514/(12 – 1) = 41.025 Degrees of freedom = df = n - 1 = 12 -1 = 11 Level of significance = a = 0.05 Part-A: Ho: Md So H1: Md > 0

Test Statistic: =t = (d – ua)/ (sa/ Vn) =t = (22 - 0)/(41.025/12) > t = 1.858 P-value: From t-distribution table; the area in the lower tail to the left of (t = 1.858) and for (df = 11), is given by: 0.0451 Hence, p-value = 0.0451 Conclusion: Since p-value is less than the significance level, reject the null hypothesis. Reject Ho. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period. Part-B: Sample mean for current year: _ x 5844 12 Sample mean for previous year: X1 =- -=487 11 to = £ x2_5580 na 12 = 465 Part-C: Percentage change in the airfare for the one-year period: 7487 = (4.85 – 1) x 100 465 = 4.7%