Anthony Wessel
Section 2
HW 1 4. (a). The observational units are the people that went on diets.

(b). The explanatory variable is the type of follow up to the diet that is randomly assigned to the observational units, and it is categorical. The response variable is whether or not the dieter regained 5 or more pounds, and this variable is categorical.

(c). This a randomized experiment because the treatments are randomly assigned to the subjects.

(d). The null hypothesis is that there is no difference between the proportion of people who regained at least 5 pounds after dieting and being treated with each of these follow-up treatments. The alternative hypothesis is that there is at least one of the proportions that are different than the other two, in that the proportion of dieters who regained at least 5 pounds is not the same as the other two proportions.

(e). The estimate of the p-value of the MAD statistic is .0008.
(f). The p-value of the chi squared statistic in this simulation is .0008, which is the same as the MAD statistic p-value.

(g). The chi squared distribution seems to fit fairly well, though it could be a little better and fit a little closer to the data. Based on the two-way table, I would expect the distributions to be pretty similar, because all of the expected counts are above 5, which means that this dataset fits the requirements for a chi squared distribution.

(h). The degrees of freedom is 2, the chi squared test statistic is 13.773 and the p-value is .001022. This p-value is very close to the p-value obtained in the simulation.

(i). The small p-value of .001022 provides strong evidence to say that these results are statistically significant under the null hypothesis, and therefore we have strong evidence to reject the null that there is no difference in the proportions of people who gained at least 5 pounds after