Q3 [11 pts] Two-way table: coffee and depression Researchers conducted a study investigating the relationship between caffeinated coffee and consumption and risk of depression in women. They collected data on 50,379 women free of depression symptoms at the start of the study in the year 1966, 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 the antidepressants. The table below shows the distribution of incidences of depression by amount of caffeinated coffee consumption. Caffeinated coffee consumption ≤1 cup/week 2-6 cup/week Clinical Yes depression No 670 373 1 cup/week 905 2-3 cup/week ≥ 4 cup/week Total 564 95 2607 11545 6244 16329 11726 2288 48132 12215 6617 17234 12290 2383 50739 (a) [1 pt] what type of test is appropriate for evaluating if there is an association between coffee intake and depression? Your answer should be the name of the test. (b) [2 pts] Write down the hypotheses for the test in part (a). (c) [2 pts] Determine the overall proportion of women who do and do not suffer from depression in this data? (d) [2 pts] Identify the expected count for the highlighted cell and calculated the contribution of this cell to the test statistic. i.e. find (observed - expected)²/expected, round your result up to 3 decimal places. (e) [2 pts] we perform a significance test, and result is provided in the following. What is the df? And what is the test statistic value from the result? data: dta X-squared = 20.932, df = p-value = 0.0003267 (f) [2 pts] From the testing result in part (e), what is your decision and conclusion at significance level 1%?