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Chapter 10: Q. T10.8 (page 699)

An SRS of size 100is taken from Population A with proportion 0.8of successes. An independent SRS of size 400is taken from Population B with proportion 0.5of successes. The sampling distribution of the difference (A 鈭� B) in sample proportions has what mean and standard deviation?

a. mean=0.3; standard deviation =1.3

b. mean=0.3; standard deviation =0.40

c. mean=0.3; standard deviation =0.047

d. mean=0.3; standard deviation =0.0022

e. mean=0.3; standard deviation =0.0002

Short Answer

Expert verified

Option (c) mean =0.3; standard deviation =0.047

Step by step solution

01

Given information

We need to find mean and standard deviation for the (A - B).

02

Simplify

As given in the question :

p1^=0.8n1=100p2^=0.5n2=400

Mean 渭=p1^-p2^=0.8-0.5=0.3

Standard deviation :

蟽=p1^(1-p1^)n1+p2^(1-p2^)n2=0.8(1-0.8)100+0.5(1-0.5)400=0.047

Therefore, option(c) is correct.

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