Question

In a survey of 2065 adults in a certain country conducted during a period of economic​ uncertainty, 64​%

thought that wages paid to workers in industry were too low. The margin of error was 4

percentage points with

95​%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

95​% confident 64​% 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 suggests that this interval sets the standard for all the other​ intervals, which is not true.

D.

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

​(b) We are 91​%

to 99​%

confident 64​%

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 suggests that this interval sets the standard for all the other​ intervals, which is not true.

C.

The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

D.

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

​(c) We are

95​%

confident that the interval from 0.60 to 0.68 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 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.

​(d) In 95​% 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 0.60 and 0.68.

Is the interpretation​ reasonable?

A.

The interpretation is reasonable.

B.

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

C.

The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

D.

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

Answer 1

Answer a. D. The interpretation is flawed. The interpretation provides no interval about the population proportion.

Explanation: A confidence interval doesn't describe the distribution of the sample data used to build the interval, so we can't say that 64​% of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low with 95% confidence

Answer b. C.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.

Explanation: When we are constructing a Confidence Interval we say that there is a % confidence that any such interval contains the parameter. There are no varing level of significances. So, this interpretation is wrong.

Answer c. A. The interpretation is reasonable.

Explanation: A confidence interval tries to capture the true value of the parameter it's estimating, which in this case is the true proportion of workers who fee that wages are too low. So, saying that the interval from 0.60 to 0.68 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 with 95% confidence is correct.

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

Explanation: A confidence interval doesn't estimate the sample result from an upcoming sample, so we can't use this interval to make predictions about the sample proportion.