Question

In the article coffee, caffeine, and risk of depression among women in the september 2011 edition of the archives of internal medicine, researchers investigated the relationship between caffeine consumption and depression among women. the participants in this study were older, with substantially lower rates of depression when compared to female teens. researchers compared two groups of women (among others) in this study: those who do not drink coffee and those who routinely drink 4 or more cups of coffee each day. for the following question, a coffee drinker is a woman who drinks four or more cups each day. the depression rate for women who do not drink coffee is 6%. for the moment, we assume that this is the rate for coffee drinkers as well. we plan to survey 920 women who drink coffee and 1100 women who do not. will the sampling distribution of differences between sample proportions be approximately normal?

Options:
a) Yes
b) No
c) Cannot be determined
d) Depends on the region sampled

Answer 1

The sampling distribution of differences between sample proportions will be approximately normal for this study.

Step-by-step explanation:

The sampling distribution of differences between sample proportions will be approximately normal if certain conditions are met. One of the conditions is that both sample sizes should be large enough, typically at least 10 or more successes and failures in each sample. Since the question states that we plan to survey 920 women who drink coffee and 1100 women who do not, both sample sizes are sufficiently large. Therefore, the sampling distribution of differences between sample proportions will be approximately normal.