The sample data below represent the number of late and on tie flights for Delta,

Question

The sample data below represent the number of late and on tie flights for Delta, United Airlines and US Airways. (Bureau of Trans. Stat. 2012)

1. Formulate the hypotheses for a test that will determine if the population proportion of late flights is the same for all three airlines.

2. Conduct the hypothesis test with .05 significance level. What is the p value and what is your conclusion?

3. Use the multiple comparison procedure to determine which population proportions differ significantly. Use a 0.05 level of significance.

Delta, united, and US Airways tBureau of iransportation Statistics, March 2012) Airlines Flight Delta United US Airways Late 51 56 On Time 26 249 344

Explanation / Answer

1) Null Hypothesis: The population proportion is of late flights is the same for all three airlines.

Alternative Hypothesis : Their is a significant difference between late fights for three sirlines.

2)

Test Statistics:

Oi is observed value

Ei is the expected value

Chi-square = 2.12

The critical value at 0.05 for (3-1)*(2-1) = 2 degrees of freedom is 5.911

P-value = 2.117

Conclusion: Since the p-value is greater that 0.05 , hence we accept null hypotheiss and conclude  population proportion is of late flights is the same for all three airlines.

Degree of freedom(DF) = K-1 DF = 2 = [ (Oi - Ei)2 / Ei ]

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