Question

In a survey of 2085 adults in a certain country conducted during a period of economic​ uncertainty, 67​% thought that wages paid to workers in industry were too low.
The margin of error was 9 percentage points with 90​% confidence.

For parts​ (a) through​ (d) below, which represent a reasonable interpretation of the survey​ results?
For those that are not​ reasonable, explain the flaw.

​(a) We are 90​% confident 67​% of adults in the country during the period of economic uncertainty
felt wages paid to workers in industry were too low.
Is the interpretation​ reasonable?

A.
The interpretation is reasonable.
B.
The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
C.
The interpretation is flawed. The interpretation provides no interval about the population proportion.
D.
The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.

​(b) We are 81​% to 99​% confident 67​% of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.
Is the interpretation​ reasonable?

A.
The interpretation is reasonable.
B.
The interpretation is flawed. The interpretation provides no interval about the population proportion.
C.
The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.
D.
The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

​(c) We are 90​% confident that the interval from 0.58 to 0.76 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low.
Is the interpretation​ reasonable?

A.
The interpretation is reasonable.
B.
The interpretation is flawed. The interpretation provides no interval about the population proportion.
C.
The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
D.
The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.

​(d) In 90​% of samples of adults in the country during the period of economic​ uncertainty, the proportion who believed wages paid to workers in industry were too low is between 0.58 and 0.76.
Is the interpretation​ reasonable?

A.
The interpretation is reasonable.
B.
The interpretation is flawed. The interpretation provides no interval about the population proportion.
C.
The interpretation is flawed. The interpretation indicates that the level of confidence is varying.
D.
The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.

Answer 1

In a survey of 2085 adults in a certain country conducted during a period of economic​ uncertainty, 67​% thought that wages paid to workers in the industry were too low.
The margin of error was 9 percentage points with 90​% confidence.

( p +- E) = ( 0.67 +- 0.09) = (0.67 -0.09 ; 0.67 +0.09 ) = ( 0.58 , 0.76)

The 90% confidence interval is (0.58 , 0.76)

​(a) We are 90​% confident 67​% of adults in the country during the period of economic uncertainty
felt wages paid to workers in the industry were too low.

Here we are not defining any confidence interval. we only gave a point estimate.

Answer:- The interpretation is flawed. The interpretation provides no interval about the population proportion.

b)

We are 81​% to 99​% confident 67​% of adults in the country during the period of economic uncertainty felt wages paid to workers in the industry were too low.
Is the interpretation​ reasonable?

No here confidence interval is varying which is not true.

Answer:- D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

c)

We are 90​% confident that the interval from 0.58 to 0.76 contains the true proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in the industry were too low.
Is the interpretation​ reasonable?

yes, it is reasonable interpretation.

Answer:- A.The interpretation is reasonable.

d) In 90​% of samples of adults in the country during the period of economic​ uncertainty, the proportion who believed wages paid to workers in the industry were too low is between 0.58 and 0.76.

Here it is stated that the sample adults.which is not reasonable.

Answer:- D.The interpretation is flawed. The interpretation suggests that this interval sets the standard for all the other​ intervals, which is not true.