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.

Answer 1

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:

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	0.23581514

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.