Does Mars, Incorporated use the same proportion of red candies in its plain and

Question

Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 52 plain M&M;'S contained 12 red candies, and another random sample of 37 peanut M&M;'S contained 5 red candies. (Use pi 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 (pl-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 ! P2 0 is not in the confidence interval, it is possible that P1 P2 We should not conclude at ere is a difference the portio of ed candies in plain and peanut M&Ms.; 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 MBMs candies in plain and peanut MBMs 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 Since the value pl-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&Ms;

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:

- 0.063 to 0.255

b) Option B is correct.

Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 12 52 5 37 0.095634096 0.081070912 -0.063261972 0.25453016

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