Question

In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty, 63 % 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 63 % 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 otherintervals, which is not true.D.The interpretation is flawed. No interval has been provided about the population proportion.(b) We are 91 % to 99 % confident 63 % 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. No interval has been provided 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 95 % confident the proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low was between 0.59 and 0.67. 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. No interval has been provided about the population proportion.D.The interpretation is flawed. The interpretation indicates that the level of confidence is varying.(d) In 9595 % 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 0.59 and 0.67. 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. No interval has been provided about the population proportion.

Answer 1

Answer:

a) D.The interpretation is flawed. No interval has been provided about the population proportion.

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

c) A.The interpretation is reasonable.

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

Step-by-step explanation:

(a) We are 95 % confident 63 % 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?

D.The interpretation is flawed. No interval has been provided about the population proportion.

The sample proportion alone will not give us any confidence in estimating the true proportion of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

We need a 95% confidence interval to claim that the true proportion is within this interval. In this case, as the margin of error is 4%, the 95% CI is 59% and 67%.

(b) We are 91 % to 99 % confident 63 % 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?

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

The confidence is set at a fixed value and from that value the confidence interval is estimated. It still uses the sample proportion instead of the confidence interval to estimate the true proportion.

(c) We are 95 % confident the proportion of adults in the country during the period of economic uncertainty who believed wages paid to workers in industry were too low was between 0.59 and 0.67. Is the interpretation reasonable?

A.The interpretation is reasonable.

It uses the right sample data and interpret correctly the meaning of the confidence interval.

(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 0.59 and 0.67. Is the interpretation reasonable?

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

This confidence interval is an estimation about the parameter of the population. It doesn't give information to estimate the sampling distribution, as it only has information of one specific sample.