Question

Researchers at P University and W State University found that airlines are doing a better job of getting passengers to their destinations on time.† AirTran Airways and Southwest Airlines were among the leaders in on-time arrivals with both having 88% of their flights arriving on time. But for the 12% of flights that were delayed, how many minutes were these flights late? Sample data showing the number of minutes that delayed flights were late are provided in the file named AirDelay. Data are shown for both airlines. Assume population variances are unknown and unequal.

AirTran

34	59	43	30	3
32	42	85	30	48
110	50	10	26	70
52	83	78	27	70
27	90	38	52	76

Southwest

45	64	42	33	66
105	45	28	38	85
75	45	33	50	63
42	35	33	64	65

(a)

Formulate the hypotheses that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let μ₁ = populationmean minutes late for delayed Airtran flights and μ₂ = population mean minutes late for delayed Southwest flights.)

(a) H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

(b) H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

     

(c) H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ = 0

(d) H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

(e) H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

(B)

What is the sample mean number of minutes late for delayed flights for each of these two airlines?

AirTran _____ min

Southwest-_____ min

(C)

Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

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

Do not reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Do not Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.     

Reject H₀. There is statistical evidence that one airline does better than the other in terms of their population mean delay time.

Reject H₀. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

Answer 1

From minitab output

Two-Sample T-Test and CI: airtan, southwest

Two-sample T for airtan vs southwest

N Mean StDev SE Mean
airtan 25 50.6 26.6 5.3
southwest 20 52.8 20.1 4.5

Difference = μ (airtan) - μ (southwest)
Estimate for difference: -2.20
95% CI for difference: (-16.25, 11.85)
T-Test of difference = 0 (vs ≠): T-Value = -0.32 P-Value = 0.754 DF = 42

a)option A

b)airtan 50.6

Southwest 52.8

c)test statistic = -0.316

P value = 0.7536

Do not reject Ho; (option a)