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 the value of the standard error of ?
A)0.0063
B)0.0794
C)0.08
D)0.10

Question

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 the value of the standard error of  ?
A)0.0063 
B)0.0794 
C)0.08 
D)0.10

Quizplus · Accepted Answer

The standard error formula for a proportion is:
SE = sqrt[p(1-p)/n]
Where p is the proportion of successes (green M&M's) and n is the sample size (25). We were given that p = 0.1 and that in our sample of 25 there were 5 green M&M's, so p-hat (the sample proportion) is 5/25 = 0.2. Plugging in these values, we get:
SE = sqrt[0.1(1-0.1)/25] = 0.0794
Therefore, the standard error is 0.0794 or approximately 0.08. The best choice is B.

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