Question

20. What do you think would happen to the variability (standard deviation) of the distribution of sample proportions if the sample size for each sample was 200 instead of 80? Explain.

Answer 1

Explanation:

Sample proportion p is the proportion of favourable numbers to total number in the sample

By central limit theorem and also approximation of binomial to normal , we have sample proportion for large number of samples will be normal

with mean = sample proportion

and std deviation =
`\sqrt{(pq)/(n) }`

Thus we find standard deviation of proportion sample is inversely proportional to the square of the sample size n.

It follows automatically that as sample size increases std deviation decreases.

Here from 80 sample size was made to 200

So std deviation would decrease automatically