A population consists of four men and one woman. The first names of the men are Adam, Bernard, Charlie, and Daniel. The first name of the woman is Elena. Suppose that the specified attribute is "male".
a. Determine the population proportion, p.
b. Complete the table below. The first column shows the possible samples of size 3, the second column gives the number of successes - the number of males obtained - for each sample, and the third column shows the sample proportion.
$\begin{array}{l} \text { Sample Number of males Sample proportion }\ \begin{array} { l l c } & \mathrm { x } & \hat { \mathrm { p } } \ \hline \text { A, B, C } & 3 & 1 \ \text { A, B, D } & 3 & 1 \ \text { A, B, E } & 2 & 2 / 3 \ \text { A, C, D } & & \ \text { A, C, E } & & \ \text { A, D, E } & & \ \text { B, C, D } & & \ \text { B, C, E } & & \ \text { B, D, E } & & \ \text { C, D, E } \end{array} \end{array}$
c. Use the third column of the table to obtain the mean of the variable $\hat { p }$. Is this mean smaller, larger, or the same as your answer in part a?. Why is this the case?

Question

A population consists of four men and one woman. The first names of the men are Adam, Bernard, Charlie, and Daniel. The first name of the woman is Elena. Suppose that the specified attribute is "male".  
a. Determine the population proportion, p. 
b. Complete the table below. The first column shows the possible samples of size 3, the second column gives the number of successes - the number of males obtained - for each sample, and the third column shows the sample proportion. 
$\begin{array}{l} \text { Sample Number of males Sample proportion }\ \begin{array} { l l c }  & \mathrm { x } & \hat { \mathrm { p } } \ \hline \text { A, B, C } & 3 & 1 \ \text { A, B, D } & 3 & 1 \ \text { A, B, E } & 2 & 2 / 3 \ \text { A, C, D } & & \ \text { A, C, E } & & \ \text { A, D, E } & & \ \text { B, C, D } & & \ \text { B, C, E } & & \ \text { B, D, E } & & \ \text { C, D, E } \end{array} \end{array}$  
c. Use the third column of the table to obtain the mean of the variable $\hat { p }$. Is this mean smaller, larger, or the same as your answer in part a?. Why is this the case?

Quizplus · Accepted Answer

The Answer of A population consists of four men and one woman. The first names of the men are Adam, Bernard, Charlie, and Daniel. The first name of the woman is Elena. Suppose that the specified attribute is "male".  
a. Determine the population proportion, p. 
b. Complete the table below. The first column shows the possible samples of size 3, the second column gives the number of successes - the number of males obtained - for each sample, and the third column shows the sample proportion. 
$\begin{array}{l} \text { Sample Number of males Sample proportion }\ \begin{array} { l l c }  & \mathrm { x } & \hat { \mathrm { p } } \ \hline \text { A, B, C } & 3 & 1 \ \text { A, B, D } & 3 & 1 \ \text { A, B, E } & 2 & 2 / 3 \ \text { A, C, D } & & \ \text { A, C, E } & & \ \text { A, D, E } & & \ \text { B, C, D } & & \ \text { B, C, E } & & \ \text { B, D, E } & & \ \text { C, D, E } \end{array} \end{array}$  
c. Use the third column of the table to obtain the mean of the variable $\hat { p }$. Is this mean smaller, larger, or the same as your answer in part a?. Why is this the case?

A Population Consists of Four Men and One Woman C Use the Third Column of the Table to Obtain