Sampling Distributions of Difference of Proportions

A candy maker offers child- and adult size bags of jelly beans with different color mixes. The company claims that the child mix has 30% red jelly beans, while the adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the child mix and a separate random sample of 100 jelly beans from the adult mix. Let p̂₁ and p̂₂ be the sample proportions of red jelly beans from the child and adult mixes, respectively. What is the shape of the sampling distribution of p̂₁ - p̂₂? Why?

• Approximately normal, because they are all greater than or equal to 10.

• Approximately normal, because they are all less than or equal to 10.

• Not approximately normal, because they are all greater than or equal to 10.

• Not approximately normal, because they are all less than or equal to 10.

A candy maker offers child- and adult size bags of jelly beans with different color mixes. The company claims that the child mix has 30% red jelly beans, while the adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the child mix and a separate random sample of 100 jelly beans from the adult mix. Let p̂₁ and p̂₂ be the sample proportions of red jelly beans from the child and adult mixes, respectively. Find the mean of the sampling distribution.

• 0.15

• -0.15

• 0.30

• There is no mean.

A candy maker offers child- and adult size bags of jelly beans with different color mixes. The company claims that the child mix has 30% red jelly beans, while the adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true. Suppose we take a random sample of 50 jelly beans from the child mix and a separate random sample of 100 jelly beans from the adult mix. Let p̂₁ and p̂₂ be the sample proportions of red jelly beans from the child and adult mixes, respectively. Calculate the standard deviation of the sampling distribution.

• 0.0740

• 0.0648

• 0.0357

• You can't calculate the standard deviation.

Your teacher brings two large bags of colored goldfish crackers to class. Bag 1 has 25% red crackers and Bag 2 has 35% red crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag 1 and a separate SRS of 40 crackers from Bag 2. Let p̂₁ - p̂₂ be the difference in the sample proportions of red crackers. What is the shape of the sampling distribution of p̂₁ - p̂₂? Why?

• Approximately normal, because they are all greater than or equal to 10.

• Approximately normal, because they are all less than or equal to 10.

• Not approximately normal, because they are all greater than or equal to 10.

• Not approximately normal, because they are all less than or equal to 10.

Your teacher brings two large bags of colored goldfish crackers to class. Bag 1 has 25% red crackers and Bag 2 has 35% red crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag 1 and a separate SRS of 40 crackers from Bag 2. Let p̂₁ - p̂₂ be the difference in the sample proportions of red crackers. Find the mean of the sampling distribution.

• 0.10

• -0.10

• 0.25

• 0.35

Your teacher brings two large bags of colored goldfish crackers to class. Bag 1 has 25% red crackers and Bag 2 has 35% red crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag 1 and a separate SRS of 40 crackers from Bag 2. Let p̂₁ - p̂₂ be the difference in the sample proportions of red crackers. Calculate the standard deviation of the sampling distribution.

• 0.0971

• 0.0612

• 0.0754

• You can't calculate the standard deviation.