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Chapter 10: Q 2. (page 639)

Literacy 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鈥檚 claim is true. Suppose we give a basic literacy test to a random sample of 60high school graduates and a separate random sample of 75high school dropouts.p^G,p^Dbe the sample proportions of graduates and dropouts, respectively, who pass the test.

a. What is the shape of the sampling distribution of p^G-p^D. Why?

b. Find the mean of the sampling distribution.

c. Calculate and interpret the standard deviation of the sampling distribution.

Short Answer

Expert verified

a. The shape is approximately normal.

b. 渭p^G-p^D=0.40

c.蟽p^G-p^D=0.07745

Step by step solution

01

Given Information

It is given that nG=60

nD=75

pG=0.80

pD=0.40

02

Shape of p^G-p^D

Assuming shape of p^G-p^Dis normal.

Conditions are:

nGpG鈮�10

nG1-pG鈮�10

nDPD鈮�10

nD1-pD鈮�10

nGpG=(60)(0.80)=48

nG1-pG=(60)(1-.80)=(60)(.20)=12

nDpD=(75)(0.40)=30

nD1-pD=(75)(1-0.40)=(75)(0.60)=45

As all four conditions are satisfied, the shape ofp^C-p^Ais approximately normal.

03

Mean of Sampling Distribution

Using 渭p^G-p^D=pG-pD

=0.80-0.40=0.40

The mean is0.40

04

Standard Deviation

High School graduates, (60)<10%of all high school graduates

Dropouts, (75)<10%of all high school graduates

Formula as: 蟽p^G-p^D=pG1-pGnG+pD1-pDnD

=0.80(1-0.80)60+0.40(1-0.40)75

=0.80(0.20)50+0.40(0.60)75鈮�0.07745

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