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 flights with their domestic airfares shown for both years.

Current Year	Previous Year
345	315
526	451
420	474
216	206
285	275
405	432
635	585
710	650
605	545
517	547
570	508
610	580

(a)

Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period.

H₀: μ_d ≤ 0

H_a: μ_d > 0

H₀: μ_d ≠ 0

H_a: μ_d = 0

    

H₀: μ_d ≥ 0

H_a: μ_d < 0

H₀: μ_d = 0

H_a: μ_d ≠ 0

H₀: μ_d < 0

H_a: μ_d = 0

Calculate the test statistic. (Use current year airfare − previous year airfare. Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

Using a 0.05 level of significance, what is your conclusion?

Reject H₀. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.Do not reject H₀. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.     Reject H₀. We cannot conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.Do not reject H₀. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.

(b)

What is the sample mean domestic airfare (in dollars) for business travel for each year?

current$ previous$

(c)

What is the percentage change in mean airfare for the one-year period? (Round your answer to one decimal place.)

Answer 1

Current Year	Previous Year	Difference
345	315	30
526	451	75
420	474	-54
216	206	10
285	275	10
405	432	-27
635	585	50
710	650	60
605	545	60
517	547	-30
570	508	62
610	580	30

∑d = 276

∑d² = 25714

n = 12

Mean , x̅d = Ʃd/n = 276/12 = 23

Standard deviation, sd = √[(Ʃd² - (Ʃd)²/n)/(n-1)] = √[(25714-(276)²/12)/(12-1)] = 41.9589

a) Null and Alternative hypothesis:

Ho : µd ≤ 0

H1 : µd > 0

Test statistic:

t = (x̅d)/(sd/√n) = (23)/(41.9589/√12) = 1.899

df = n-1 = 11

p-value = T.DIST.RT(1.8989, 11) = 0.0421

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

Reject H0. We can conclude that there has been a significant increase in the mean domestic airfare for business travel for the one-year period.

b)

For Current Year :

∑x = 5844, n1 = 12

Mean , x̅1 = Ʃx/n = 5844/12 = 487

For Previous Year :

∑x = 5568, n2 = 12

Mean , x̅2 = Ʃx/n = 5568/12 = 464

c)

Percentage change in mean airfare for the one-year period = ((487-464)/464) *100 = 4.96 = 5.0%