
Sampling Distribution of Difference Between Two Proportions
Authored by Barbara White
Mathematics
11th - 12th Grade

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6 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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.
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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.
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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.
4.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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.
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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
6.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
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.
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