Comparing Two Proportions Textbook Section 10.1

Sampling Distribution of a Difference between Two Proportions

Sampling Distribution of Two Proportions

What about the sampling distribution of p 1 – p 2 ?

Check Your Understanding

Confidence Intervals for p 1 – p 2

Example  As part of the Pew Internet and American Life Project, researchers conducted two surveys in The first survey asked a random sample of 799 U.S. teens about their use of social media and the Internet. The second survey posed similar questions to a random sample of 2253 U.S. adults. In these two studies, 80% of teens and 69% of adults used social-networking sites.  Describe the distribution of the difference of the proportions?  Shape?  Center?  Spread?

Four Steps for a Confidence Interval

Significance Tests for p 1 – p 2  A observed difference between two sample proportions can reflect an actual difference in the parameters OR it may just be due to chance. Significance testing will help us determine which makes more sense.  Hypotheses: H 0 : p 1 – p 2 = hypothesized value  For our purposes, we’ll limit ourselves to cases where there is no hypothesized difference  Thus, H 0 : p 1 – p 2 = 0 OR H 0 : p 1 = p 2  The alternative hypothesis indicates what kind of difference we expect.

Significance Test Example  Researchers wanted to compare the proportion of students who come to school without breakfast between two elementary schools. An SRS of 80 students from School 1 found that 19 had not eaten breakfast. At School 2, an SRS of 150 students included 26 who had not eaten breakfast. Both schools have more than 1500 students.  Hypotheses:  H 0 : p 1 – p 2 = 0  H a : p 1 – p 2 ≠ 0  Where p 1 is the proportion of students who go without breakfast at School 1 and p 2 is the proportion of students w/o breakfast at School 2

Example Continued