Question

You may need to use the appropriate technology to answer this 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.

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	65	42	34	67
104	45	27	38	84
76	44	33	51	63
42	35	34	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 = 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?

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?

Reject H₀. There is 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.    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.

Answer 1

The statistical software output for this problem is:

Hence,

a) Hypotheses: Option D is correct.

b) Sample means:

Company A = 50.6 min

Company B = 52.85 min

c) Test statistic = -0.314

p-value = 0.7551

Conclusion: Option B is correct.