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: H0:H0:Caffeinated coffee consumption and depression in women are independent. HA:HA: Caffeinated coffee consumption and depression in women are dependent/associated. 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: between 0.1 and 0.05 between 0.05 and 0.025 between 0.025 and 0.01 less than 0.01 Use your results to evaluate the hypotheses from the problem above Select one: Since p ≥ α we reject the null hypothesis and accept the alternative Since p<α we reject the null hypothesis and accept the alternative Since p ≥ α we accept the null hypothesis Since p ≥ α we do not have enough evidence to reject the null hypothesis 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
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:
- H0:H0:Caffeinated coffee consumption and depression in women are independent.
HA:HA: Caffeinated coffee consumption and depression in women are dependent/associated. - 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:
- between 0.1 and 0.05
- between 0.05 and 0.025
- between 0.025 and 0.01
- less than 0.01
Use your results to evaluate the hypotheses from the problem above
Select one:
- Since p ≥ α we reject the null hypothesis and accept the alternative
- Since p<α we reject the null hypothesis and accept the alternative
- Since p ≥ α we accept the null hypothesis
- Since p ≥ α we do not have enough evidence to reject the null hypothesis
- 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
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