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 60 plain M&M'S contained 15 red candies, and another random sample of 38 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 ________

Solutions

Expert Solution

Solution :

Given that,

= x₁ / n₁ = 15 / 60 = 0.25

1- = 0.75

= x₂ / n₂ = 9 / 38 = 0.237

1 - = 0.763

At 95% confidence level the z is ,

Z_/2 = 1.96

95% confidence interval for p₁ - p₂ is ,

( - ) Z_/2 * [(1- ) / n₁ + (1 - ) / n₂]

(0.25 - 0.237) * [(0.25 * 0.75) / 60 + (0.237 * 0.763) / 38]

-0.161 < p₁ - p₂ < 0.187

-0.161 to 0.187

orchestra answered 1 year ago

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