0 Question 1 B 01'1pt O3 1399 Details You intend to conduct a goodness-of-fit test for a multinomial distribution with 4 categories. You collect data from 5? subjects. What are the degrees of freedom for the 3:2 distribution for this test? d.f. = | 0 Question 2 a on pt 03 5399 Details You are conducting a multinomial Chi-Square Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies: Complete the table. Report all answers accurate to three decimal places. Ho:pA = 0.5; p3 = 0.1;pg = 0.3; p0 = 0.1 :::::. A 43 |_| a 34 |:| c 29 |:| n 13 |:| What is the chi-square test-statistic for this data? x2=| What is the P-V'alue? P-Value = I For significance level alpha 0.005. What would be the conclusion of this hypothesis test? 0 Reject the Hull Hypothesis 0 Fail to reject the Hull Hypothesis There is to show that at least one of the category proportions is different. Report all answers accurate to three decimal places. Question Hel p: [E] Video 0 Question 1 E 0l1 pt '0 3 3 99 G) Details You intend to conduct a test of homogeneity for a contingency table with 3 categories in the column variable and 3 categories in the row variable. You collect data from 59? subjects. What are the degrees of freedom for the X2 distribution for this test? d.f. = I I Question Help: 75"] Written Example 0 Question 2 a on pt 0 3 c: 99 G) Details You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table. xIv 2| ABBI'IS 4s| B 42|4r 3r| Give all answers rounded to 2 places after the decimal point, if necessary. {a} Enter the expected frequencies below: 4|; A |_ .| I. III .| .| |._.| |._.| lb} What is the chi-square test-statistic for this data? Test Statistic: X2 = I I X {c} What is thep-value for this test of independence P-Value: = I I {d} What is the correct conclusion of this hypothesis test at the 0.025 significance level? Ci- There is sufficient evidence to support the claim that the row and column variables are dependent. Ci- There is not sufficient evidence to support the claim that the row and column variables are dependent. {:21- There is sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. Ci- There is not sufficient evidence to warrant rejection of the claim that the row and column variables are dependent. Remember to give all answers rounded to 3 places after the decimal point, if necessary: Question Help: [E] Video . Question 3 0/1 pt O 3 2 99 0 Details 6.48 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. (M. Lucas et al, 2011) Tip: Do NOT include the TOTAL row and column in your table when you copy into your technology application such as Statcrunch or a Calculator. $ 1 2-6 2-3 24 Total cup/week cups/week cup/day cups/day cups/day Clinical 905 Depression: Yes 670 373 564 95 2607 Clinical Depression: No 11545 6244 16329 11726 2288 48132 Total 12215 6617 17234 12290 2383 50739 a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression? Ot-test O Chi-squared goodness of fit test O Chi-squared test for independence O ANOVA b) Write the hypotheses for the test you identified in part a) O Ho: Coffee consumption and clinical depression in women are independent of one another Ha: Coffee consumption and clinical depression in women are associated OHo: H = 0 Ha: H = 0 OH: X2 = 0 Ha: X2 = 0 c) Calculate the overall proportion of women who do and do not suffer from depression: (round to four decimal places) Depression: No Depression: d) Identify the expected count for the cell corresponding to individuals with clinical depression and who drink 2-6 cups of coffee per week. Then calculate the contribution of this cell to the test statisitc, i.e. (Observed - Expected)2 / Expected Observed: Expected: Contribution to test statistic: e) The test statistic for the hypothesis test is x2=20.93. What is the p-value? O.05 s p