Chapter 6, Section 3-D, Exercise 132 Consider random samples of size 286 drawn f

Question

Chapter 6, Section 3-D, Exercise 132 Consider random samples of size 286 drawn from population A with proportion 0.13 and random samples of size 312 drawn from population B with proportion 0.32. (a) Find the standard error of the distribution of differences in sample proportions, PA-PB Round your answer for the standard error to three decimal places. standard error the absolute tolerance is +/-0.001 LINK TO TEXT (b) Are the sample sizes large enough for the Central Limit Theorem to apply? O Yes O No

Explanation / Answer

a)

p1 = 0.13, p2 = 0.32

Standard error = Sqrt( p1(1-p1) / n1 + p2( 1-p2) / n2 )

= sqrt (0.13 * 0.87 / 286 + 0.32 * 0.68 / 312)

= 0.033

b)

In order to central limit theorem hold, sample size must be sufficiently large, that is sample size >= 30.

Since n1 >= 30 and n2 >= 30,

Yes, sample sizes large enough for the Central Limit Theorem to apply.

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