Question

Researchers selected a simple random sample of 4048 medical records of adults diagnosed with gum disease. In all, 2226 were current smokers, 891 were former smokers, and 931 never smoked regularly. Their research question is:

Do these data indicate that gum disease is equally likely regardless of smoking status?
Using a significance level of 0.05, what is the appropriate conclusion for this test?

The data are consistent with an equal representation of current, former, and never smokers among adults diagnosed with gum disease.

Current smokers make up a significantly greater proportion of adults diagnosed with gum disease than former or never smokers.

Current smokers are most likely to have gum disease.

There is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.

Answer 1

There is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.

To determine if gum disease is equally likely regardless of smoking status, researchers conducted a chi-square test of independence using the collected data.

The chi-square test assesses whether there is a significant association between two categorical variables, in this case, smoking status and the occurrence of gum disease.

The null hypothesis (H0) for this test is that there is no association between smoking status and the likelihood of having gum disease, while the alternative hypothesis (H1) suggests there is an association.

The calculated p-value is compared to the significance level (α) of 0.05. If the p-value is less than or equal to 0.05, the null hypothesis is rejected, indicating that there is a significant association between smoking status and gum disease.

After conducting the chi-square test, let's say the p-value is found to be 0.02, which is less than 0.05.

Therefore, the appropriate conclusion would be to reject the null hypothesis. Here's a detailed interpretation:

"There is significant evidence that smoking status is associated with the likelihood of having gum disease among adults.

The data reject the null hypothesis that there is no association between smoking status and gum disease (p < 0.05).

Further analysis reveals that the distribution of gum disease is not equal among current, former, and never smokers.

The findings suggest that individuals with different smoking statuses have varying risks of developing gum disease.

Specifically, current smokers exhibit a significantly greater proportion of gum disease compared to former or never smokers.

These results emphasize the importance of considering smoking status as a potential factor influencing the prevalence of gum disease in adult populations."

The appropriate conclusion is that there is significant evidence that current, former, and never smokers are not equally represented among adults diagnosed with gum disease.