Question

Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 59 plain M&M'S contained 13 red candies, and another random sample of 31 peanut M&M'S contained 9 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 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 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 very unlikely 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 very unlikely that p₁ = p₂. We should conclude that there is a difference in the proportion of red candies in plain and peanut M&M'S.

Answer 1

Answer a)

A 95% confidence interval for the difference in the proportions of red candies for the plain and peanut varieties (p1 − p2) is -0.448 to 0.115

Answer b)

Correct answer is:

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