Question

Does Mars, Incorporated use the same proportion of red candies in its plain and peanut varieties? A random sample of 53 plain M&M'S contained 12 red candies, and another random sample of 34 peanut M&M'S contained 6 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. You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

= 12/53 = 0.226

= 6/34 = 0.176

The pooled sample proportion(P) = ( * n1 + * n2)/(n1 + n2)

                                                     = (0.226 * 53 + 0.176 * 34)/(53 + 34)

                                                     = 0.206

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval is

() +/- z_0.025 * sqrt(P(1 - P)(1/n1 + 1/n2))

= (0.226 - 0.176) +/- 1.96 * sqrt(0.206 * (1 - 0.206) * (1/53 + 1/34))

= 0.05 +/- 0.174

= -0.124, 0.224

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 .