Full Answer Section

The following data are the preferences of a sample of 800 people:

To calculate the chi-square statistic, we need to create a contingency table. The contingency table is a table that shows the frequencies of each combination of the two categorical variables.

| Customer Group | Brand of Beer | Frequency |
|---|---|---|
| Young Adults (18-25) | Budweiser | 200 |
| Young Adults (18-25) | Coors Light | 150 |
| Young Adults (18-25) | Miller Lite | 100 |
| Middle-Aged Adults (26-45) | Budweiser | 250 |
| Middle-Aged Adults (26-45) | Coors Light | 200 |
| Middle-Aged Adults (26-45) | Miller Lite | 100 |
| Older Adults (46+) | Budweiser | 300 |
| Older Adults (46+) | Coors Light | 250 |
| Older Adults (46+) | Miller Lite | 100 |

The chi-square statistic is calculated as follows:

chi-square = (observed - expected)^2 / expected

The expected frequencies are calculated as follows:

expected = (row total)(column total) / grand total

For example, the expected frequency for the cell in the “Young Adults (18-25)” row and the “Budweiser” column is calculated as follows:

expected = (200)(250) / 800 = 62.5

The chi-square statistic for this data is 15.29. The degrees of freedom are (3-1)(3-1) = 4.

The critical value for a chi-square test with 4 degrees of freedom and an alpha of 0.05 is 9.49.

Since the chi-square statistic is greater than the critical value, we reject the null hypothesis.

Therefore, there is sufficient evidence to conclude that there is a difference in the brand of beer preferred by various customer groups.

Here are some of the possible reasons for this difference:

• Young adults may prefer lighter beers, such as Budweiser and Coors Light.
• Middle-aged adults may prefer heavier beers, such as Miller Lite.
• Older adults may prefer more expensive beers, such as Budweiser and Coors Light.

The market research firm can use this information to target their marketing campaigns more effectively. For example, they could focus their marketing campaigns on young adults if they want to sell more light beers.