Question

The success of an airline depends heavily on its ability to provide a pleasant customer experience. One dimension of customer service on which airlines compete is on-time arrival. The tables below contain a sample of data from delayed flights showing the number of minutes each delayed flight was late for two different airlines, Company A and Company B.

Company A

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


Company B

46 63 43 33 65

104 45 27 39 84

75 44 34 51 63

42 34 34 65 64


Required:

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.

Answer 1

To test for a difference between the population mean minutes late for delayed flights by Company A and Company B, we can formulate the following hypotheses:

Null Hypothesis (H0): There is no significant difference between the population mean minutes late for delayed flights by Company A and Company B.

Alternate Hypothesis (Ha): There is a significant difference between the population mean minutes late for delayed flights by Company A and Company B.

To statistically test these hypotheses, we can perform an independent samples t-test. The t-test will compare the means of the two samples and determine if the difference between them is statistically significant or due to chance.

In this case, we can consider the minutes late for delayed flights by Company A as one sample and the minutes late for delayed flights by Company B as the other sample. We can calculate the mean and standard deviation of each sample and use these values to perform the t-test.

Based on the results of the t-test, if the p-value is less than the predetermined significance level (usually 0.05), we would reject the null hypothesis and conclude that there is a significant difference between the population mean minutes late for delayed flights by Company A and Company B. If the p-value is greater than or equal to the significance level, we would fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference.

Note: To perform the t-test, we would also need to assume that the samples are independent, the populations are approximately normally distributed, and the variances of the populations are equal. These assumptions should be checked before conducting the t-test.