Question

Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties?...

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.

Homework Answers

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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