Question

According to the Department of Education:

• 27% of adults over the age of 65 in the United States have earned at least a bachelor's degree
• 36% of adults 25 to 34 years old in the United States have earned at least a bachelor's degree

Suppose these proportions are true for the respective populations.   

A researcher is planning on the following samples:
A random sample of 200 adults over the age of 65 will be selected and their highest degree will be recorded.
A random sample of 200 adults 25 to 34 years old will be selected and their highest degree will be recorded.

Let p̂₁represent the proportion of adults over the age of 65 in the sample who have earned at least a bachelor’s degree.
Let p̂₂ represent the proportion of adults 25 to 34 years old in the sample who have earned at least a bachelor’s degree.

What is the approximate probability that a random sample of 200 adults over the age of 65 and a random sample of adults 25 to 34 years old will result in a difference in sample proportion, p̂₁- p̂₂ , of at most -0.01?

• 0.0154

• 0.0418

• 0.9582

• 0.9846

4.e

0.5 point(s)

The researcher has decided to triple the sample size for both groups:

A random sample of 600 adults over the age of 65 will be selected and their highest degree will be recorded.
A random sample of 600 adults 25 to 34 years old will be selected and their highest degree will be recorded.  

The increase in sample sizes, from 200 to 600, will _________________ the expected value of all possible values of the differences in sample proportions, p̂₁- p̂₂.

• increase

• decrease

• not affect

4.f

0.5 point(s)

The researcher has decided to triple the sample size for both groups:

A random sample of 600 adults over the age of 65 will be selected and their highest degree will be recorded.
A random sample of 600 adults 25 to 34 years old will be selected and their highest degree will be recorded.  

The increase in sample sizes, from 200 to 600, will _________________ the value of the standard deviation of all possible values of the differences in sample proportions, p̂₁- p̂₂.

• increase

• decrease

• not affect

Answer 1