91Ó°ÊÓ

A population consists of three men Jose, Peter, Carlo and two women Gail and Frances. Specified attribute is "Female".

As per the given information, group has three men and two women. Specified attribute is being a female.

Therefore, number of success is \(x=2\) and population size is \(n=5\).

So, population proportion would be \(p=\frac{x}{n}=\frac{2}{5}=0.4\).

As per the given information, group has three men and two women. Specified attribute is being a female. Sample proportion size is \(n=5\).

A table is created with all the possible samples of size \(5\).

From part (a) of this exercise, Population proportion is \(p=0.4\).

From part (b) of this exercise, sample proportion is obtained for each sample of size \(5\) and below dot plot is created.

From part (a) of this exercise, Population proportion is \(p=0.4\).

From part (b) of this exercise, sample proportion is obtained for each sample of size \(5\).

Mean of sample proportions, \(\mu _{\hat{p}}=\frac{\sum \hat{p}}{10}\)

\(\Rightarrow \mu _{\hat{p}}= \frac{0.4}{1}\)

\(\Rightarrow \mu _{\hat{p}}= 0.4\)

From part (a) of this exercise, Population proportion is \(p=0.4\) .

From part (b) of this exercise, mean of sample proportions, \(\mu _{\hat{p}}= 0.4\)

Both value are same because, the mean of all sampling distribution, \(\hat{p} \) , is same as the population proportion, \(p\).