Does Mars, Incorporated use the same proportion of red candies in its plain and
ID: 3371911 • Letter: D
Question
Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 54 plain M&M'S contained 12 red candies, and another random sample of 33 peanut M&M'S contained 5 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 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 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 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 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.
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 will be:
(-0.094, 0.236)
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.
Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 12 54 5 33 0.070707071 0.084240358 -0.094400997 0.23581514Related Questions
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