Estimating the Difference between Two Population Proportions
Question 3 • CA-Statistics and Probability B
A therapist wanted to determine if yoga or meditation is better for relieving stress. The therapist recruited 100 of her high-stress patients. Fifty of them were randomly assigned to take weekly yoga classes, and the other 50 were assigned weekly meditation classes. After one month, 30 of the 50 patients in the yoga group reported less stress, and 35 of the 50 patients in the meditation group reported less stress.Based on the 95% confidence interval, (–0.29, 0.09), is there convincing evidence of a difference in the true proportions of patients experiencing stress relief in the yoga and meditation groups?
Answer
A
There is convincing evidence because the two sample proportions are different.
B
There is convincing evidence because the difference in the two sample proportions is –0.10. Since this is not 0, there is a difference in the true proportion of patients practicing yoga and patients practicing meditation who would experience stress relief.
C
There is not convincing evidence because the interval contains 0.
D
There is not convincing evidence because the interval contains both negative and positive values for the true difference.
Explanation
The 95% confidence interval for the difference in the true proportions is (–0.29, 0.09), and it includes 0. A difference of 0 is consistent with the data, so the interval does not provide convincing evidence that the true proportions differ. Therefore, the correct choice is “There is not convincing evidence because the interval contains 0.”
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