Question

part f is the attached graph

Sampling Distributions 0.8 0.6 0.4 0.2 0 Population Prop. of 1s 0.72 Population 704 60 50 40 30 20 10 Samples Sample size Prop. of 1s 100 0.68 Samples 100 80 60 40 20 Sample prop. of 1s #of Samples Mean Median Std. dev. 1000 0.7207 0.72 0.0456 il 00.2 0.40.60.8 Sample proportions Why do you think that this graph from part (f) has the shape you described? Use the Central Limit Theorem large sample size condition to answer this question in one sentence. Explicitly show these calculations.

Answer 1

Given the shape of the distribution of the sample proportions of 1's is approximately normal.

According to central limit theorem as the sample size becomes sufficiently large, the sampling distribution of sample proportion tends to approximately normal with mean "p" and standard deviation of $\sqrt{\frac{p(1-p)}{n}}$

where n- the sample size,

p-population proportion.

Therefore the mean of the sample proportion of 1s is p=0.72

standard deviation

$\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.72*(1-0.72)}{1000}}$

$\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.72*0.28}{1000}}$

$\sqrt{\frac{p(1-p)}{n}}=\sqrt{0.0002016}$

$\sqrt{\frac{p(1-p)}{n}}=0.0142$

standard deviation=0.0142