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In the following questions, random samples of the given size are drawn from the populations with the given proportions. For each question, a) find the mean and standard error of the distribution of differences in sample proportions pˆa−pˆb, b) indicate if the sample sizes is large enough for the Central Limit Theorem to apply. Give your answers to 4 decimal places.

Samples of size 80 from population A with proportion 0.35 and samples of size 20 from population B with proportion 0.11.
Mean:
Std. Error:
Are the sample sizes large enough for the Central Limit Theory to apply?
i.. i. Yes ii.. ii. No
Samples of size 500 from population A with proportion 0.81 and samples of size 2000 from population B with proportion 0.65.
Mean:
Std. Error:
Are the sample sizes large enough for the Central Limit Theory to apply?
i.. i. Yes ii.. ii. No
Samples of size 40 from population A with proportion 0.63 and samples of size 20 from population B with proportion 0.29.
Mean:
Std. Error:
Are the sample sizes large enough for the Central Limit Theory to apply?
i.. i. Yes ii.. ii. No

Sagot :

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