Warm Up A 2011 paper asked a random sample of students from Stanford University to consider the following statement: “The meeting next Wednesday has been moved forward two days.” The statement is ambiguous, the meeting could now be on either Monday or Friday. The students’ guesses as to which day the meeting is are below. Monday Friday 11 33 Is this convincing evidence the proportion that would guess Monday or Friday is not the same?

Two Way Tables Summary of head injuries among college students 0 1 2 or more Total Soccer Players 45 25 21 91 Non-Soccer Athletes 68 15 13 96 Non-Athletes 45 5 3 53 Total 158 45 37 240 Is this convincing evidence the proportions of individuals with head injuries are different among soccer players, non-soccer athletes and non-athletes?

Practice - Two Way Tables A 2005 study involved 290 people who had lost at least 10% of their body weight in a medical weight-loss program. They were randomly assigned to a follow-up group that either met monthly in person, met monthly online or received a monthly newsletter. After 18 months the amount of weight regained was measured. Regain < 5 lbs Regain > 5 lbs In-person 54 47 Online 44 53 Letter 25 67 Make a two-way table of observed and expected values for the hypothesis that the proportion who gained more than 5 lbs is the same for all methods of follow-up.

Practice – Chi Square Test for Homogeneity A 2005 study involved 290 people who had lost at least 10% of their body weight in a medical weight-loss program. They were randomly assigned to a follow-up group that either met monthly in person, met monthly online or received a monthly newsletter. After 18 months the amount of weight regained was measured. Regain < 5 lbs Regain > 5 lbs In-person 54 47 Online 44 53 Letter 25 67 Is this statistically significant data that the proportion of people gaining 5 pounds or more is different among the 3 follow-up programs?

Practice A 2005 study took a random sample of overweight preschool students and a separate random sample of non-overweight preschool students. For each sample it was determined how many sweet drinks they consumed per day. The data is below. 0 1 2 3 or more Overweight 22 73 56 102 Not 93 207 168 339 Is there evidence of a difference in the proportion of overweight preschool kids consuming 0, 1, 2, or 3+ sweet drinks versus kids who are not?