Exam 9: Comparing More Than Two Proportions

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -What is the shape of the resulting null distribution of MAD statistics shown in the output of the Multiple Proportions applet?

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Use the Goodness of Fit applet to conduct a simulation-based chi-square goodness-of-fit test using the chi-square statistic, and report the statistic and the p-value. Use at least 1000 shuffles. chi-square statistic = p-value =

Researchers analyzed eating behavior and obesity at Chinese buffets. They estimated people's body mass indexes (BMI) as they entered the restaurant then categorized them into three groups---bottom third (lightest), middle third, and top third (heaviest). One variable they looked at was whether or not they browsed the buffet (looked it over) before serving themselves or served themselves immediately. Treating the BMI categories as the explanatory variable and whether or not they browsed first as the response, the researchers wanted to see if there was an association between BMI and whether or not they browsed the buffet before serving themselves. They found the following results: • Bottom Third: 35 of the 50 people browsed first • Middle Third: 24 of the 50 people browsed first • Top Third: 17 of the 50 people browsed first -Compute the Mean Group Diff statistic.

Hope student researchers want to determine if students yawning (when being yawned at) is asso-ciated with the time of day (morning, afternoon, and evening). They found the following results when they yawned in front of people around campus: • Morning: 25 of the 39 people yawned • Afternoon: 15 of the 38 people yawned • Evening: 29 of the 44 people yawned -For each time of day, calculate the conditional proportion of people that yawned and write these numbers as decimals not fractions. Morning___________ Afternoon____________ Evening____________

What shape is the distribution of the chi-square statistic?

Are people equally likely to be born on any day of the seven days of the week? Or are some days more likely to be a person's birthday than other days? To investigate this question, days of birth were recorded for the 147 "noted writers of the present" listed in The World Almanac and Book of Facts 2000. The counts for the seven days of the week are given in the following table. -Let ?_day be the probability that a person is born on a particular day. What is the null hypothesis?