A chewing gum manufacturer wishes to determine if his customers prefer one flavor gum to any other flavor. He selects a random sample of customers and records the flavor of gum that is purchased. Compute the test value for the data given.

Question

Quizplus · Accepted Answer

In order to determine if customers have a preference for one flavor of gum over another, we can conduct a chi-square goodness of fit test. The null hypothesis is that there is no preference for any particular flavor, while the alternative hypothesis is that there is a preference.

To find the test value, we first need to calculate the expected frequencies under the null hypothesis. Let's say we have four flavors of gum: peppermint, spearmint, cinnamon, and fruit. If we assume that customers are equally likely to choose any flavor, then we would expect each flavor to have a frequency of 25% (or 0.25, since we have four flavors). We can multiply this by the sample size to get the expected frequency for each flavor.

For example, if our sample size is 100, we would expect 25 customers to choose peppermint, 25 to choose spearmint, 25 to choose cinnamon, and 25 to choose fruit. If we actually observed 30 customers choosing peppermint, 20 choosing spearmint, 25 choosing cinnamon, and 25 choosing fruit, we can calculate the chi-square test statistic as follows:

((30-25)^2/25) + ((20-25)^2/25) + ((25-25)^2/25) + ((25-25)^2/25) = 2.24 + 1 + 0 + 0 = 3.24

The degrees of freedom for a chi-square goodness of fit test are equal to the number of categories minus one (df = 4-1 = 3, in this case). Using a chi-square distribution table or calculator, we can find the p-value associated with a test statistic of 3.24 and 3 degrees of freedom. The p-value turns out to be approximately 0.36.

Since the p-value is greater than our chosen level of significance (usually 0.05), we fail to reject the null hypothesis and conclude that there is not enough evidence to say that customers have a preference for one flavor of gum over another.

A Chewing Gum Manufacturer Wishes to Determine If His Customers