Omega-3 fatty acids are essential to the function of the human body, with evidence suggesting that they help lower the risk of heart disease and other blood disorders through their role in suppressing inflammation and increasing blood flow. Omega-3 fatty acids are one of the only types of fats the body cannot make on its own, so we must get them from food. Although a blood test can determine the level of omega-3 fatty acids in the bloodstream, it would save time and money if simply knowing about a person’s diet (specifically fish consumption, since some fish contain high amounts of omega-3 fatty acids) could help predict the omega-3 fatty acid blood levels. In recent research (Jackson et al., 2018), researchers conducted a small study to see whether a person’s fish consumption could help predict their omega-3 fatty acid blood levels, potentially saving time and money by not needing to get omega-3 fatty acid levels measured via a blood test. The file Omega-3 contains the omega-3 fatty acid blood levels (as a percentage of total fatty acids in the blood), where the subjects were split into the following five groups according to the amount of fish they report consuming: A: <1 times/month; B: 2–3 times/month; C: 1 time/week; D: 2 times/week; E: >2 times/week. We want to determine whether the omega-3 fatty acid levels differ in these groups of people. 

a. Identify the explanatory and response variables, and describe the type (categorical or quantitative) of each. 

b. State the hypotheses in words or symbols. 

c. Put the data into the Multiple Means applet and report the five mean blood levels. Did people that eat the most fish have the highest omega-3 fatty acid levels? Did those that eat the least amount of fish have the lowest omega-3 fatty acid levels? 

d. Determine the value of the Mean Group Diff statistic. 

e. Use simulation-based inference to find a p-value and determine if there is strong evidence of an association between the amount of fish someone consumes and his or her omega-3 fatty acid blood levels.