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# Statistics: Solving an ANOVA

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For the time being, the air traffic control system in the United States is run by the federal government. Some people would like to change this, arguing that the air traffic control system should be part of the private sector.

Among the arguments given for the privatization of air traffic control is that flight delays are much too common in the United States. A first step in deciding if, indeed, delays in the U.S. are "too common" might be to compare flight delay information from the U.S. and other nations.

Suppose that you have in front of you information from several samples of flights over the past six weeks. Each sample is composed of domestic flights for a certain country. (One of the samples is composed of flights within the U.S., one of the samples is composed of flights within Canada, and so on.) The information recorded for each flight is the time (in minutes) that the plane was late to the arrival gate. (If the plane was early, then the time recorded is negative.)

Based on this information, you perform a one-way, independent-samples ANOVA test of the hypothesis that there are no differences in the mean flight delay times among the several countries. The results of this ANOVA test are summarized in the ANOVA table below. Complete the missing cell in the ANOVA table (round your answer to at least two decimal places), and then answer the questions.

Source of Variance Degree of Freedom Sum of Squrares Mean square FStat
treatment between
groups 2 1015.4 507.7 ?

Error w/in groups 661 68929.7 104.3

Total 663 69945.1

Questions:
1. How many flights total were sampled in the study?

2. For the ANOVA test, it is assumed that the population variance of flight delay times are equal for each country studied. What is an unbiased estimate of this common population variance based on the sample variances?

3. What is the p-value corresponding to the f statistic for the ANOVA test? Round answer to 3 decimal places. Using the 0.05 level of significance, can you conclude from the test that there are differences among the countries in mean flight delay times?