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

For Company A, sample 1 :  
x̅1 =   50.6
s1=   26.56596
n1 =   25
For Company B, sample 2 :  
x̅2 =   52.85
s2 =   20.01914
n2 =    20
α =    0.05

a) Null and Alternative hypothesis:
Ho : µ1 - µ2 = 0
Ha : µ1 - µ2 ≠ 0

b) x̅1 - x̅2 = 50.6 -52.85 = -2.25

c) Pooled variance :  
S²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2)  
=   570.9897

Test statistic:              
t = (x̅1 - x̅2)/[√(s²p(1/n1 + 1/n2 )]              
= -0.314

df = n1+n2-2 = 43   
              
p-value :              
At t = -0.314 and df = 43, two tailed p-value =T.DIST.2T(-0.3139, 43) = 0.7551

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.