Question

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.

	Coffee	≤ 1	2-6	1	2-3	≥ 4
	Consumption	cup/week	cups/week	cup/day	cups/day	cups/day	Total
Clinical	Yes	670	373	905	564	95	2,607
depression	No	11,545	6,244	16,329	11,726	2,288	48,132
	Total	12,215	6,617	17,234	12,290	2,383	50,739

What hypotheses are appropriate for evaluating if there is an association between coffee intake and depression?

Select one:

1. H0:H0:Caffeinated coffee consumption and depression in women are independent.
   HA:HA: Caffeinated coffee consumption and depression in women are dependent/associated.
2. H0:H0:Caffeinated coffee consumption and depression in women are dependent/associated.
   HA:HA: Caffeinated coffee consumption and depression in women are independent.

What proportion of the women from this study ended up suffering from depression?

What proportion of the women from this study never suffered from depression?

Calcuate the expected number that correspons to the observed number 95

Only with your number from the question above and the number 95, perform the operation
(O−E)^2 /E

How many degrees of freedom are there in this situation?

The test statistic is χ2=20.93χ2=20.93 What is the p-value?

Select one:

1. between 0.1 and 0.05
2. between 0.05 and 0.025
3. between 0.025 and 0.01
4. less than 0.01

Use your results to evaluate the hypotheses from the problem above

Select one:

1. Since p ≥ α we reject the null hypothesis and accept the alternative
2. Since p<α we reject the null hypothesis and accept the alternative
3. Since p ≥ α we accept the null hypothesis
4. Since p ≥ α we do not have enough evidence to reject the null hypothesis
5. Since p<α we fail to reject the null hypothesis

One of the authors of this study was quoted on the NYTimes as saying it was “too early to recommend that women load up on extra coffee” based on just this study. Do you agree with this statement? Explain your reasoning

Answer 1

1)

H0:Caffeinated coffee consumption and depression in women are independent.

HA: Caffeinated coffee consumption and depression in women are dependent/associated.

2)

proportion of the women from this study ended up suffering from depression =48132/50739 =0.9486

3)

expected number =row total*column total/grand total =(2607*2383)/50739 =122.44

(O−E)^2 /E =(95-122.44)^2/122.44=6.150

4)

degree of freedom =(row-1)*(column-1) =(2-1)*(5-1)=4

5) less than 0.01

6)

Since p<α we reject the null hypothesis and accept the alternative

since from given data we can not conclude that load up on extra coffee decrease prevalence of depression.