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Chapter 10: Q. 25 (page 625)

Construct and interpret a 95% confidence interval for p1-p2 in Exercise 23. Explain what additional information the confidence interval provides.

Short Answer

Expert verified

We are 95% confident that the proportion difference is between 0.100 and0.382.

Step by step solution

01

Given Information

Given

x1=44

n1=88

x2=21

n2=81

02

Explanation

The sample proportion is the number of successes divided by the sample size:

p^1=x1n1=4488=0.5

p^2=x2n2=2181鈮�0.259

For confidence level 1-伪=0.95, determine z伪/2=z0.025using table II (look up 0.025in the table, the z-score is then the found z-score with opposite sign):

z伪/2=1.96

The endpoints of the confidence interval for p1-p2are then:

localid="1650451164119" p^1-p^2-z伪/2路p^11-p^1n1+p^21-p^2n2=(0.5-0.259)-1.960.5(1-0.5)88+0.259(1-0.259)81鈮�0.100

localid="1650451174743" p^1-p^2+z伪/2路p^11-p^1n1+p^21-p^2n2=(0.5-0.259)+1.960.5(1-0.5)88+0.259(1-0.259)81鈮�0.382

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