Question

2.   Data, which may be found in the Excel file named “Luggage” on the course Canvas Site (Chapter 10 Data Files), gives the weights (in pounds) of randomly selected checked bags for an airline’s International and Domestic flights on the same day.

1. • First, test to determine if the variances in weights of checked bags differ between international and domestic flights. Show and follow the 7 steps for hypothesis testing. (8 points)
   • Verify your results in part a. using Minitab; attach or include your output. (3 points)
   • Using the information from your test results in part a., test to determine if the average weight for bags on an international flight is greater than the average weight for bags on a domestic flight. (8 points).
   • Refer to part c., give and interpret the p-value using probabilities. (4 points)
   • Verify your results in part c., using Minitab; attach or include your output. (3 points)

   • International	Domestic
     39	29
     54	36
     46	33
     39	34
     69	38
     47	37
     48	33
     28	29
     54	43
     62	39
     	43
     	42
     	32
     	35
     	39

Answer 1

  

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5. Decision = Reject Ho, Since 6.74 is greater than 3.21

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6 . P-value = 0.002

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7. Conclusion = we have enough evidence to conclude that population variances are not equal.

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Minitab output

Test and CI for Two Variances: International, Domestic

Method

σ₁: standard deviation of International

σ₂: standard deviation of Domestic

Ratio: σ₁/σ₂

F method was used. This method is accurate for normal data only.

Descriptive Statistics

Variable	N	StDev	Variance	95% CI for σ²
International	10	11.890	141.378	(66.888, 471.191)
Domestic	15	4.580	20.981	(11.246, 52.185)

Ratio of Variances

Estimated Ratio	95% CI for Ratio using F
6.73839	(2.100, 25.592)

Test

Null hypothesis	H₀: σ₁² / σ₂² = 1
Alternative hypothesis	H₁: σ₁² / σ₂² ≠ 1
Significance level	α = 0.05

Method	Test Statistic	DF1	DF2	P-Value
F	6.74	9	14	0.002

Test and CI for Two Variances: International, Domestic

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2.

Two-Sample T-Test and CI: International, Domestic

Method

μ₁: mean of International

µ₂: mean of Domestic

Difference: μ₁ - µ₂

Equal variances are not assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
International	10	48.6	11.9	3.8
Domestic	15	36.13	4.58	1.2

Estimation for Difference

Difference	95% Lower Bound for Difference
12.47	5.32

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ > 0

T-Value	DF	P-Value
3.16	10	0.005

Since p-value is less than 0.05 so, reject the null hypothesis and we can conclude that the International mean is greater than Domestic mean