Question

Three randomly selected households are surveyed. The numbers of people in the households are

11​,

33​,

and

88.

Assume that samples of size

nequals=2

are randomly selected with replacement from the population of

11​,

33​,

and

88.

Construct a probability distribution table that describes the sampling distribution of the proportion of

oddodd

numbers when samples of sizes

nequals=2

are randomly selected. Does the mean of the sample proportions equal the proportion of

oddodd

numbers in the​ population? Do the sample proportions target the value of the population​ proportion? Does the sample proportion make a good estimator of the population​ proportion? Listed below are the nine possible samples.

11​,11   

11​,33   

11​,88   

33​,11   

33​,33   

33​,88   

88​,11   

88​,33   

88​,88

  

Construct the probability distribution table.

Sample Proportion	Probability
▼ 0.25 0.1 0	nothing
▼ 0.25 0.75 0.5	nothing
▼ 0.25 1 0.75	nothing

​(Type an integer or​ fraction.)

Choose the correct answer below.

A.The proportion of

eveneven

numbers in the population is equal to the mean of the sample proportions of

oddodd

numbers.

B.The proportion of

oddodd

numbers in the population is equal to the mean of the sample proportions.

C.The proportion of

oddodd

numbers in the population is not equal to the mean of the sample proportions.

D.The proportion of

oddodd

numbers in the population is equal to the mean of the sample proportions of

eveneven

numbers.

Choose the correct answer below.

A.The sample proportions target the proportion of

oddodd

numbers in the​ population, so sample proportions make good estimators of the population proportion.

B.The sample proportions do not target the proportion of

oddodd

numbers in the​ population, so sample proportions make good estimators of the population proportion.

C.The sample proportions target the proportion of

oddodd

numbers in the​ population, so sample proportions do not make good estimators of the population proportion.

D.The sample proportions do not target the proportion of

oddodd

numbers in the​ population, so sample proportions do not make good estimators of the population proportion.

Click to select your answer(s).

Answer 1

sample proportion		probability
0		1/9
0.5		4/9
1		4/9

B.The proportion of odd numbers in the population is equal to the mean of the sample proportions.

A.The sample proportions target the proportion of odd numbers in the​ population, so sample proportions make good estimators of the population proportion.