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Chapter 10: Q. 8 (page 666)

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 for the difference (Population A – Population 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 role="math" localid="1650371687597" =-0.3; standard deviation =0.047

(e) mean =0.3; standard deviation=0.0002

Short Answer

Expert verified

The sampling distribution for the difference (Population A – Population B) in sample proportions has option (c) mean=0.3; standard deviation=0.047

Step by step solution

01

Given information

Population A is100

Successes is0.8

Population B is400

Successes is0.5

02

Explanation

The given data is

p^1=0.8

n1=100

p^2=0.5

n2=400

The mean of the sampling distribution is the difference in sample proportions:

localid="1650387643052" μ=p^1-p^2=0.8-0.5=0.3

The standard deviation is

localid="1650387684458" σ=p^p1-p^p1n1+1n2=0.8(1-0.8)100+0.5(1-0.5)400≈0.047.

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