"Mouth Piercings May Cause Gums to Recede" reported in 2005 that "researchers at Ohio State University looked at 58 young adults with an average age between 21 and 22. Half had pierced lips and the other half did not, although both groups were otherwise alike in age and gender. Among the subjects with a pierced lip, 41.4 percent had receding gums, although only 6.9 percent of those without a pierced lip suffered from this periodontal condition."8

a. Set up a two-way table of observed counts, based on information provided in the article, and construct a table of expected counts.

b. Calculate the chi-square statistic.

c. Comment on whether or not the data should convince us of a relationship between pierced lips and receding gums.

d. In your table of expected counts, find the expected proportions with receding gums for those who have pierced lips and for those who do not. Explain why these expected proportions are equal.

e. What two possible confounding variables were taken into account in the design of the study?

f. Which of these additional variables may also have played a role in whether or not a young adult had pierced lips and whether or not he or she had receding gums: smoking, or attentiveness to hygiene, or both, or neither? Explain.

g. Which one of the following focuses on data production?

1. Experts conclude that for all students, those with pierced lips are more likely to suffer from receding gums than those who don't have pierced lips.

2. In order to make a comparison, researchers attempted to look at two samples of students who were similar in important ways.

3. The observed counts are quite different from the expected counts.

4. A difference as large as the one observed is very unlikely to have come about by chance.

h. Which one of the statements in part (g) focuses on displaying and summarizing data?

i. Which one of the statements in part (g) focuses on probability?

j. Which one of the statements in part (g) focuses on statistical inference?

k. The article mentions that "in the piercedlip group, recession of the gumline was, on average, twice as deep as it was among those with no pierced lip." Tell whether the variables of interest here arequantitative or categorical, and identify each as being explanatory or response.

l. The article also mentions that "the longer a subject had had a pierced lip, the more likely it was that he or she suffered from gum recession." Tell whether the variables of interest here are quantitative or categorical, and identify each as being explanatory or response.

m. Suppose we wanted to use the sample proportion of students without a pierced lip who had receding gums to set up a confidence interval for the population proportion. Explain why an interval based on a z multiplier may not be very accurate.