In an article published in Lancet (2001), researchers shared their findings from a study where they followed 6,272 Swedish men for 30 years to see whether there was an association between the amount of fish in the diet and likelihood of prostate cancer. The results are presented in the following two-way table:

a. Is this an experiment or an observational study? How are you deciding?

b. Identify the observational units.

c. Identify the explanatory and response variables. Also, for each variable, identify whether it is categorical or quantitative.

d. Define the parameters of interest. Assign symbols to these parameters.

e. State the appropriate null and alternative hypotheses in symbols.

f. State the appropriate null and alternative hypotheses in words.

g. Explain why it would be okay to use the theory-based method to find a p-value for this study.

h. Use an appropriate applet (for example, the Multiple Proportions applet) to find and report the following from the data: (i) the name of the statistic and its numeric value and (ii) the theory based p-value.

i. Interpret the p-value in the context of the study.

j. State a complete conclusion about this study, including significance, causation, and generalization. Be sure to explain how you are arriving at your conclusion.

k. If relevant, use an applet to find and report a set of confidence intervals appropriate for the context. Also, interpret the confidence intervals in the context of the study. If not relevant, explain why it is not particularly useful to look at confidence intervals for the parameter(s) of interest in the context of this study.

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Large Moderate Small None Total Yes Prostate cancer? 42 209 14 201 466 2,769 2,420 507 110 5,806 No Total 549 2,621 6,272 2,978 124