Consider random samples of size 58 drawn from population A with proportion 0.78 and random samples of size 76 drawn from population B with proportion 0.68 .
(a) Find the standard error of the distribution of differences
in sample proportions, p^A-p^B.
Round your answer for the standard error to three decimal places.
standard error = Enter your answer in accordance to the question statement
(b) Are the sample sizes large enough for the Central Limit Theorem to apply?
first sample size, n1=58
proportion success of sample 1 , p̂1=0.78
second sample size, n2 = 76
proportion success of sample 1 , p̂ 2=x2/n2 = 0.68
Std error , SE = SQRT(p̂1 * (1 - p̂1)/n1 + p̂2 * (1-p̂2)/n2) = √(0.78*(1-0.78)/58 + 0.68*(1-0.68)/76) = 0.076(answer)
b. Yes sample size is large enough to apply central limit theorem
please revert for doubts
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