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 cup/week 2-6 cups/week 1 cup/day 2-3 cups/day ≥ 4 cups/day Total Clinical Depression: Yes 670 373 905 564 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? Chi-squared goodness of fit test ANOVA Chi-squared test for independence t-test Write the hypotheses for the test you identified in part a) Ho: Coffee consumption and clinical depression in women are independent of one another Ha: Coffee consumption and clinical depression in women are associated Ho: Χ2 = 0 Ha: Χ2 ≠ 0 Ho: μ = 0 Ha: μ ≠ 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 χ2=20.93. What is the p-value? p < .01 p ≥ .1 .01 ≤ p < .05 .05 ≤ p < .1 f) What is the conclusion of this test? There is enough evidence to claim an association between coffee intake and clinical depression in women There is not enough evidence to claim an association between coffee intake and clinical depression in women There is no association between coffee intake and clinical depression in women Drinking more coffee makes women less depressed

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 cup/week 2-6 cups/week 1 cup/day 2-3 cups/day ≥ 4 cups/day Total Clinical Depression: Yes 670 373 905 564 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? Chi-squared goodness of fit test ANOVA Chi-squared test for independence t-test Write the hypotheses for the test you identified in part a) Ho: Coffee consumption and clinical depression in women are independent of one another Ha: Coffee consumption and clinical depression in women are associated Ho: Χ2 = 0 Ha: Χ2 ≠ 0 Ho: μ = 0 Ha: μ ≠ 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 χ2=20.93. What is the p-value? p < .01 p ≥ .1 .01 ≤ p < .05 .05 ≤ p < .1 f) What is the conclusion of this test? There is enough evidence to claim an association between coffee intake and clinical depression in women There is not enough evidence to claim an association between coffee intake and clinical depression in women There is no association between coffee intake and clinical depression in women Drinking more coffee makes women less depressed

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

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ISBN:9780079039897

Author:Carter

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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 cup/week	2-6 cups/week	1 cup/day	2-3 cups/day	≥ 4 cups/day	Total
Clinical Depression: Yes	670	373	905	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?

Chi-squared goodness of fit test
ANOVA
Chi-squared test for independence
t-test

Write the hypotheses for the test you identified in part a)

H_o: Coffee consumption and clinical depression in women are independent of one another
H_a: Coffee consumption and clinical depression in women are associated
H_o: Χ² = 0
H_a: Χ² ≠ 0
H_o: μ = 0
H_a: μ ≠ 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 χ²=20.93. What is the p-value?

p < .01
p ≥ .1
.01 ≤ p < .05
.05 ≤ p < .1

f) What is the conclusion of this test?

There is enough evidence to claim an association between coffee intake and clinical depression in women
There is not enough evidence to claim an association between coffee intake and clinical depression in women
There is no association between coffee intake and clinical depression in women
Drinking more coffee makes women less depressed

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