b. Express the null hypothesis in symbols. (Hint: Remember that hypotheses are always about parameters, so define and use appropriate symbols for parameters.) HO: opt in = opt out = neutral Ha: opt in ? opt out ? neutral 5. Researchers found that 23 of 55 subjects in the opt-in group chose to be organ donors, 41 of 50 in the opt-out group chose to be organ donors, and 44 of 56 in the neutral group chose to be organ donors. a. Based on these counts, produce a two-way table of counts, putting the explanatory variable in columns. (Hint: You have seen this table earlier in this chapter!) Organ donor Opt in Opt out neutral yes 23 41 44 no 32 9 12 b. For each of the three groups, calculate the conditional proportion who agreed to become an organ donor. opt in: 23/55 =.418 opt out: 41/50 =.82; neutral: 44/56 =.786 c. Produce a segmented bar graph (by hand or with the Multiple Proportions applet) to compare these conditional proportions across the three groups. N/A d. Comment on what your calculations and graph reveal about whether the default option used in the question appears to affect how likely the person is to become an organ donor. The default option has a positive affect if the person is to become a We see some differences in the sample proportions of individuals who chose to be organ donors across the three treatments, but are these differences large enough to be statistically significant? In other words, do these data provide strong evidence of an association between donor recruiting strategy (opt-in, opt-out, neutral) and choosing to become an organ donor in the population