Coffee and Depression. Researchers conducted a study investigating the relationship between caffeinated coffee consumption and risk of depression in women. They collected data on 50,739 women free of depression symptoms at the start of the study in the year 1996, and these women were followed through 2006. The researchers used questionnaires to collect data on caffeinated coffee consumption, asked each individual about physician-diagnosed depression, and also asked about the use of antidepressants. The table below shows the distribution of incidences of depression by amount of caffeinated coffee consumption.
(a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression?
(b) Write the hypotheses for the test you identified in part (a).
(c) Calculate the overall proportion of women who do and do not suffer from depression.
(d) Identify the expected count for the highlighted cell, and calculate the contribution of this cell to the test statistic, i.e. (Observed Expected) 2/Expected.
(e) The test statistic is x2 = 20.93. What is the p-value?
(f) What is the conclusion of the hypothesis test?
(g) One of the authors of this study was quoted on the NY Times as saying it was "too early to recommend that women load up on extra coffee" based on just this study.64 Do you agree with this statement? Explain your reasoning.