3. Researchers have noted a decline in cognitive functioning as people age (Bartus, 1990). However, the results from other research suggests that the antioxidants in foods such as blueberries can reduce and even reverse these age-related declines, at least in laboratory rats (Joseph et al., 1999). Based on these results, one might theorize that the same antioxidants might also benet elderly humans. Suppose a researcher is interested in testing this theory. The researcher obtains a sample of n = 16 adults who are older than 65, and gives each participant a daily dose of a blueberry supplement that is very high in antioxidants. After taking the supplement for 6 months, the participants are given a standardized cognitive skills test and produce M = 54. For the general population of elderly adults, scores on the test average u = 50 and form a normal distribution with o = 12. Do the data from this sample provide evidence that the blueberry supplement increases cognitive skills among elderly people? Using a one- tail test with a = .05. a. State the null hypothesis in words and in a statistical form. (1) b. State the alternative hypothesis in words and a statistical form. (1) c. Compute the appropriate statistic to test the hypotheses. Sketch the distribution with the standard error and locate the critical region with the critical value (3). d. State your statistical decision. (.5) e. Compute Cohen's d to measure the size of the effect. Interpret what this effect size really means in this context. (2) f. What is your conclusion? (don't forget the statistical information). (1) 9. Given your statistical decision (in part d), what type of decision error could you have made (.5)