The candy company that makes M&M's claims that 10% of the M&M's it produces are green.Suppose that the candies are packaged at random,and the small bags contain 25 M&M's.When we randomly pick a bag of M&M's,we may assume that this represents a simple random sample of size n = 25.Suppose that in a randomly selected small bag of M&M's,there are 5 green M&M's.What is a 99% plus four confidence interval for p,the population proportion of green M&M's?
A)(0,0.4061)
B)(0.0161,0.4283)
C)(0.0367,0.4461)
D)(0.0856,0.3971)

Question

Quizplus · Accepted Answer

We can use a one-sample proportion confidence interval since we are interested in estimating the population proportion of green M&M's. The formula for the confidence interval is:

p̂ ± z*√(p̂(1-p̂)/n)

where p̂ is the sample proportion, z* is the z-score corresponding to the level of confidence (99% plus four gives us a level of 103%), and n is the sample size.

Using the given values, we have:

p̂ = 5/25 = 0.2
z* = 2.576 (from standard normal table or calculator)
n = 25

Plugging in these values, we get:

0.2 ± 2.576*√(0.2(1-0.2)/25)
0.2 ± 0.205
(0.0367, 0.4461)

Therefore, the 99% plus four confidence interval for p is (0.0367, 0.4461), which is closest to choice C.

The Candy Company That Makes M&M's Claims That 10% of the M&M's