Test: Module 4 exam

Question 16

This Test: 20 pts possible

The ages (years) of three government officials when they died in office were

54

,

45

,

and

61

.

Complete parts (a) through (d).

a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples.

A.

left parenthesis 54 comma 54 right parenthesis comma left parenthesis 54 comma 45 right parenthesis comma left parenthesis 54 comma 61 right parenthesis comma left parenthesis 45 comma 54 right parenthesis comma left parenthesis 45 comma 45 right parenthesis comma left parenthesis 45 comma 61 right parenthesis comma left parenthesis 61 comma 54 right parenthesis comma left parenthesis 61 comma 45 right parenthesis comma left parenthesis 61 comma 61 right parenthesis

B.

left parenthesis 54 comma 45 right parenthesis comma left parenthesis 54 comma 61 right parenthesis comma left parenthesis 45 comma 54 right parenthesis comma left parenthesis 45 comma 61 right parenthesis comma left parenthesis 61 comma 54 right parenthesis comma left parenthesis 61 comma 45 right parenthesis

C.

left parenthesis 54 comma 54 right parenthesis comma left parenthesis 54 comma 45 right parenthesis comma left parenthesis 54 comma 61 right parenthesis comma left parenthesis 45 comma 45 right parenthesis comma left parenthesis 45 comma 61 right parenthesis comma left parenthesis 61 comma 61 right parenthesis

D.

left parenthesis 54 comma 45 right parenthesis comma left parenthesis 54 comma 61 right parenthesis comma left parenthesis 45 comma 61 right parenthesis

b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution.

Sample Range

Probability

0

nothing

54

nothing

61

nothing

122

nothing

(Type an integer or a fraction.)

c. Compare the population range to the mean of the sample ranges. Choose the correct answer below.

A.

The population range is equal to the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

B.

The population range is not equal to the mean of the sample ranges (it is also not equal to the age of the oldest official or age of the youngest official at the time of death).

C.

The population range is equal to the age of the oldest official at the time of death and the mean of the sample ranges is equal to the youngest official at the time of death.

D.

The population range is equal to the mean of the sample ranges.

d. Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators of population ranges? Why or why not?

A.

The sample ranges do not target the population range, therefore, sample ranges do not make good estimators of population ranges.

B.

The sample ranges target the population range, therefore, sample ranges do not make good estimators of population ranges.

C.

The sample ranges target the population range, therefore, sample ranges make good estimators of population ranges.

D.

The sample ranges do not target the population range, therefore, sample ranges make good estimators of population ranges.