Question

Researchers at two universities found that airlines are doing a better job of getting passengers to their destinations on time. Company A and Company B 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 shown below for both airlines. Use Excel to run a two-sample t-test assuming unequal variances to answer the questions.

Company A

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

Company B

44	63	41	32	67
104	46	27	39	84
74	44	33	51	62
43	36	32	65	66

(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 = population mean minutes late for delayed Company A flights and μ₂ = population mean minutes late for delayed Company B flights.)

H₀: μ₁ − μ₂ ≤ 0

H_a: μ₁ − μ₂ > 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

    

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

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? (Round your answers to two decimal places.)

Company A minCompany B 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 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.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.

Answer 1

t-Test: Two-Sample Assuming Unequal Variances
	Company A	Company B
Mean	50.6	52.65
Variance	705.75	399.6078947
Observations	25	20
Hypothesized Mean Difference	0
df	43
t Stat	-0.295245657
P(T<=t) one-tail	0.384613587
t Critical one-tail	1.681070704
P(T<=t) two-tail	0.769227174
t Critical two-tail	2.016692173