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 10 red candies, and another random sample of 33 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 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

p1(hat)=10/59=0.1694

n1= 59

p2(hat)=7/33=0.2121

n2= 33

pooled sample proportion is

p= 0.18478

standard error of the test:

SE=0.084368087

Alpha=0.05 Zalpha/2= 1.96

margin of error =zalpha/2*SE=0.165361451

lower bound of confidence interval=(p1-p2)-MOE

=-0.2079

upper bound of confidence interval=(p1-p2)+MOE

=0.1227

95 % confidence interval is between

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

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