Question

The Department of Transportation would like to investigate if differences exist in the proportions of flights that arrive on-time for Alaska Airlines, Delta Airlines, Southwest Airlines, and United Airlines. The following data represent the number of on-time flights from random samples taken from each airline.

Alaska Delta Southwest United
Number on-time 90 95 95 60
Sample size 100 120 100 80

The chi-square test statistic for these samples is _____.

Answer 1

To investigate the differences in proportions of on-time flights for different airlines, we can use a chi-square test statistic. The chi-square test statistic measures the discrepancy between observed and expected frequencies. Using the provided data, we can calculate the chi-square test statistic as 1.23.

Step-by-step explanation:

To investigate if differences exist in the proportions of flights that arrive on-time for different airlines, we can use a chi-square test statistic. The chi-square test statistic measures the discrepancy between the observed frequencies and the expected frequencies. In this case, we have data on the number of on-time flights and the sample size for each airline.

To calculate the chi-square test statistic, we first calculate the expected frequencies for each airline based on the total number of on-time flights and the total sample size. Then, we calculate the chi-square value by summing the squared difference between the observed and expected frequencies, divided by the expected frequencies.

Using the provided data, we can calculate the chi-square test statistic as follows:

Expected frequency for Alaska = (90/100) x (380/400) = 85.5

Expected frequency for Delta = (95/120) x (380/400) = 94.5

Expected frequency for Southwest = (95/100) x (380/400) = 90.5

Expected frequency for United = (60/80) x (380/400) = 71.25

Chi-square test statistic = ((90-85.5)2/85.5) + ((95-94.5)2/94.5) + ((95-90.5)2/90.5) + ((60-71.25)2/71.25) = 1.23