Domestic Airfare. The Global Business Travel Association...

Domestic Airfare. The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years. a. Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period. What is the $p$ -value? Using a .05 level of significance, what is your conclusion? b. What is the sample mean domestic airfare for business travel for each year? c. What is the percentage change in the airfare for the one-year period?

Domestic Airfare. The Global Business Travel Association reported the domestic airfare for business travel for the current year and the previous year. Below is a sample of 12 flights with their domestic airfares shown for both years.
a. Formulate the hypotheses and test for a significant increase in the mean domestic airfare for business travel for the one-year period. What is the $p$ -value? Using a .05 level of significance, what is your conclusion?
b. What is the sample mean domestic airfare for business travel for each year?
c. What is the percentage change in the airfare for the one-year period?

Key Concepts

Percentage Change Calculation

Percentage change is calculated to quantify the proportional difference between the two values. It is computed by taking the difference between the current and previous values, dividing by the previous value, and multiplying by 100 to express the result as a percentage. This calculation provides insight into the magnitude of change over time.

Sample Mean Calculation

Calculating the sample mean involves summing the observed values in a sample (in this context, the domestic airfares for each year) and dividing by the number of observations. This provides a measure of central tendency, showing the average airfare for each year in the sample.

p-value and Significance Level

The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. In hypothesis testing, if the p-value is below a predetermined significance level (commonly 0.05), the null hypothesis is rejected, indicating that the observed difference is statistically significant.

Hypothesis Testing

Hypothesis testing involves formulating a null hypothesis (typically stating that there is no effect or no difference, such as no increase in airfare) and an alternative hypothesis (stating that there is an increase in airfare). The paired t-test then uses sample data to determine if there is enough evidence to reject the null hypothesis in favor of the alternative.

Paired t-test

A paired t-test is a statistical method used to compare two related samples, such as measurements taken from the same unit (e.g., the same flights) at two different time points. It accounts for the fact that the observations are not independent, and it tests whether the mean difference between the paired observations is significantly different from zero.

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