Does Mars, Incorporated use the same proportion of red candies in its plain and
ID: 3062554 • Letter: D
Question
Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 57 plain M&M'S contained 13 red candies, and another random sample of 34 peanut M&M'S contained 7 red candies. (Use p1 for the proportion of red candies in plain M&M'S and p2 for the proportion of red candies in peanut M&M'S.)
(a) Construct a 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties (p1 p2). (Round your answers to three decimal places.) to
(b) Based on the confidence interval in part (a), can you conclude that there is a difference in the proportions of red candies for the plain and peanut varieties? Explain.
Since the value p1 p2 = 0 is in the confidence interval, it is possible that p1 = p2. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.
Since the value p1 p2 = 0 is not in the confidence interval, it is possible that p1 = p2. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.
Since the value p1 p2 = 0 is not in the confidence interval, it is possible that p1 = p2. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.
Since the value p1 p2 = 0 is in the confidence interval, it is possible that p1 = p2. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.
Explanation / Answer
The statistical software output for this problem is:
Two sample proportion summary confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
95% confidence interval results:
Hence,
a) 95% confidence interval: (-0.152, 0.196)
b) Since the value p1 p2 = 0 is in the confidence interval, it is possible that p1 = p2. We should not conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S. Option A is correct.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 13 57 7 34 0.022187822 0.088866982 -0.15198826 0.19636391Related Questions
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