Question

Page 3 of 18 MyOpenMath Assessment 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) 31 2-623 24 Total Total cup/week eups/week cupiday cups/day cupo/day Clinical 373 905 564 95 2607 Depression: Clinical No 670 6244 16329 11726 2288 48132 1507391 Depression: 11545 Totalーーf-12215ー士ー6617 ー士 172341 12290 2383 2383 50739 a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression? O Chi-squared goodness of fit test OANOVA OChi-squared test for independence Ot-test b) Write the hypotheses for the test you identified in part a) OHo: Coffee consumption and clinical depression in women are independent of one another H.: Coffee consumption and clinical depression in women are associated e) Calculate the overall proportion of women who do and do not suffer from depression (round to four decimal places) No Depression: https://www.myopenma php 12/6/2018

Answer 1

Observed number table:

Expected numbers =

For example : expected number for (depression and <=1 ) is (2607*12215/50739) = 627.614

Expected numbers table :

a) To find the association between two categorical variables we use Chi square test for independence.

Answer: Chi square test for independence.

b) According to chi square test for independence.

H0 : Coffee consumption and clinical depression in women are independent of one another.

Ha : Coffee consumption and clinical depression in women are associated.

c) Proportion for depression = Row total depression / Overall total

= 2607 / 50739

Proportion for depression = 0.0514

Proportion for No depression = Row total No depression / Overall total

= 48132 / 50739

Proportion for No depression = 0.9486

d) Observed value for ( depression and 2-6 cups coffee ) = 373

Expected value for ( depression and 2-6 cups coffee ) = 339.9854

Contribution to test statistic = ( Observed - expected )²/ Expected = 3.2059

e) $\chi$ ² = 20.93 , We can find p- value using excel function =CHIDIST(  $\chi$² , degrees of freedom )

Degrees of freedom = (r-1)*(c-1) , r are number of rows excluding total and c are number of columns excluding total

r = 2 and c = 5

Degrees of freedom = (2-1)*(5-1) = 1*4 = 4

=CHIDIST( 20.93,4 )= 0.00033

So P<=0.01

f) conclusion of the test : Since p value is less than 0.01 , we reject H0 . so supposed to accept Ha.

There is enough evidence to claim an association between Coffee consumption and clinical depression in women.