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.

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 |

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 μ_{1} = populationmean
minutes late for delayed Airtran flights and μ_{2} =
population mean minutes late for delayed Southwest flights.)

(a) H_{0}: μ_{1} − μ_{2} = 0

H_{a}: μ_{1} − μ_{2} ≠ 0

(b) H_{0}: μ_{1} − μ_{2} ≠ 0

H_{a}: μ_{1} − μ_{2} = 0

(c) H_{0}: μ_{1} − μ_{2} < 0

H_{a}: μ_{1} − μ_{2} = 0

(d) H_{0}: μ_{1} − μ_{2} ≤ 0

H_{a}: μ_{1} − μ_{2} > 0

(e) H_{0}: μ_{1} − μ_{2} ≥ 0

H_{a}: μ_{1} − μ_{2} < 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 *H*_{0}. There is no statistical
evidence that one airline does better than the other in terms of
their population mean delay time.

Do not Reject *H*_{0}. There is statistical
evidence that one airline does better than the other in terms of
their population mean delay time.

Reject *H*_{0}. There is statistical evidence
that one airline does better than the other in terms of their
population mean delay time.

Reject *H*_{0}. 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)

AirTran
Southwest
34
45
59
64
43
42
30
33
3
66
32
105
42
45
85
28
30
38
48
85
110
75
50
45
10
33
26
50
70
63
52
42
83
35
78
33
27
64
70
65
27
90
38
52
76
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