SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
Do Now:
1.
2.
SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
The Sampling Distribution of  − 
C hoose an SRS of size n1 from Population 1 with proportion of successes p1 and an independent
SRS of size n2 from Population 2 with proportion of successes p 2.
Shape:
Center:
Spread: The standard deviation of the sampling distribution of  −  is
SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
Example:
Suppose that there are two large high schools, each with more than 2000 students, in a certain
town. At School 1, 70% of students did their homework last night. Only 50% of the students at
School 2 did their homework last night. The counselor at School 1 takes an SRS of 100 students
and records the proportion 1 that did homework. School 2’s counselor takes an SRS of 200
students and records the proportion 2 that did homework. School 1’s counselor and School 2’s
counselor meet to discuss the results of their homework surveys. After the meeting, they both
report to their principals that 1 − 2 = 0.10.
(a) Describe the shape, center, and spread of the sampling distribution of  − 
(b) Find the probability of getting a difference in sample proportions  −  of 0.10 or
less from the two surveys. Show your work.
(c) Does the result in part (b) give us reason to doubt the counselors’ reported
value? Explain.
SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
You Try!
Your teacher brings two bags of colored goldfish crackers to class. She tells you that Bag 1 has
25% red crackers and Bag 2 has 35% red crackers. Each bag contains more than 500
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 1 − 2 be the difference in the sample proportions of
red crackers.
(a) What is the shape of the sampling distribution of 1 − 2?
(b) Find the mean and standard deviation of the sampling distribution. Show your work.
(c) Find the probability that 1 − 2 is less than or equal to −0.02. Show your work.
(d) Based on your answer to Question 3, would you be surprised if the difference in the
proportion of red crackers in the two samples was 1 − 2 = −0.02? Explain.
SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
LESSON PRACTICE
1. A candy maker offers C hild and Adult bags of jelly beans with different color mixes. The
company claims that the C hild 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 C hild mix and a separate random sample of 100 jelly beans from the
Adult mix.
(a) Find the probability that the proportion of red jelly beans in the C hild sample is less than or
equal to the proportion of red jelly beans in the Adult sample. Show your work.
(b) Suppose that the C hild and Adult samples contain an equal proportion of red jelly beans.
Based on your result in part (a), would this give you reason to doubt the company’s claim?
Explain.
SWBAT: Interpret the Sampling Distribution of a Difference between Two Proportions
Lesson 10-1
2. A researcher reports that 80% of high school graduates but only 40% of high school dropouts
would pass a basic literacy test. Assume that the researcher’s claim is true. Suppose we give a
basic literacy test to a random sample of 60 high school graduates and a separate random
sample of 75 high school dropouts.
(a) Find the probability that the proportion of graduates who pass the test is at least 0.20
higher than the proportion of dropouts who pass. Show your work.
(b) Suppose that the difference in the sample proportions (graduate – dropout) who pass the
test is exactly 0.20. Based on your result in part (a), would this give you reason to doubt the
researcher’s claim? Explain