Question

Skittles: The popular Skittles candy comes in 5 colors. According to the Skittles website, the colors are evenly distributed in the population of Skittle candies. So each color makes up 20% of the population. Suppose that we buy 2 small bags of Skittles. We determine the percentage of green Skittles in one bag and the percentage of orange Skittles in the other bag. Suppose that each bag contains 40 candies. We define the difference in sample proportions as "green" minus "orange." Which of the following will give a sample difference of 0.10?

a. Bag 1 has 12% green Skittles, Bag 2 has 8% orange Skittles.
b. Bag 1 has 15% green Skittles, Bag 2 has 5% orange Skittles.
c. Bag 1 has 20% green Skittles, Bag 2 has 10% orange Skittles.
d. Bag 1 has 10% green Skittles, Bag 2 has 20% orange Skittles

Answer 1

To calculate the sample difference, calculate the proportion of green Skittles in the first bag and the proportion of orange Skittles in the second bag. Subtract the proportion of orange Skittles from the proportion of green Skittles to get the sample difference. None of the given options will give a sample difference of 0.10.

Step-by-step explanation:

To calculate the sample difference, we need to find the proportion of green Skittles in the first bag and the proportion of orange Skittles in the second bag. We can then subtract the proportion of orange Skittles from the proportion of green Skittles to get the sample difference.

Let's calculate the sample difference for each option:

a. Bag 1 has 12% green Skittles, Bag 2 has 8% orange Skittles:
Sample difference = 12% - 8% = 4% (Not 0.10)

b. Bag 1 has 15% green Skittles, Bag 2 has 5% orange Skittles:
Sample difference = 15% - 5% = 10% (Not 0.10)

c. Bag 1 has 20% green Skittles, Bag 2 has 10% orange Skittles:
Sample difference = 20% - 10% = 10% (Not 0.10)

d. Bag 1 has 10% green Skittles, Bag 2 has 20% orange Skittles:
Sample difference = 10% - 20% = -10% (Not 0.10)

None of the options will give a sample difference of 0.10.