Step 1

Given that in a survey of 2085 adults in a certain country conducted during a period of economic \(\displaystyle{63}\%\) thought that wages paid to workers in industry were too low. The margin of error was 8 percentage points with \(\displaystyle{90}\%\) confidence.

Given values are

Margin of error \(\displaystyle{\left({M}\right)}={8}\%={0.08}\)

\(\displaystyle\hat{{{p}}}={63}\%={0.63}\)

We are \(\displaystyle{90}\%\) confident \(\displaystyle{63}\%\) of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

The confidence interval for \(\displaystyle{90}\%\) confident is

\(\displaystyle{C}.{I}.={\left(\hat{{{p}}}-{M},\ \hat{{{p}}}+{M}\right)}\)

\(\displaystyle{C}.{I}.={\left({0.63}-{0.08},\ {0.63}+{0.08}\right)}\)

\(\displaystyle{C}.{I}.={\left({0.55},\ {0.71}\right)}\)

Here population proportion is not mention in this interval so

The correct option is

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

Step 2

We are \(\displaystyle{82}\%\) to \(\displaystyle{98}\%\) confident \(\displaystyle{63}\%\) of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

The correct option is

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

Step 3

We are \(\displaystyle{90}\%\) confident that the interval from 0.55 to 0.71 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.

The correct option is

A) The interpretation is reasonable.

Step 4

In \(\displaystyle{90}\%\) 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 0.55 and 0.71.

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

Given that in a survey of 2085 adults in a certain country conducted during a period of economic \(\displaystyle{63}\%\) thought that wages paid to workers in industry were too low. The margin of error was 8 percentage points with \(\displaystyle{90}\%\) confidence.

Given values are

Margin of error \(\displaystyle{\left({M}\right)}={8}\%={0.08}\)

\(\displaystyle\hat{{{p}}}={63}\%={0.63}\)

We are \(\displaystyle{90}\%\) confident \(\displaystyle{63}\%\) of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

The confidence interval for \(\displaystyle{90}\%\) confident is

\(\displaystyle{C}.{I}.={\left(\hat{{{p}}}-{M},\ \hat{{{p}}}+{M}\right)}\)

\(\displaystyle{C}.{I}.={\left({0.63}-{0.08},\ {0.63}+{0.08}\right)}\)

\(\displaystyle{C}.{I}.={\left({0.55},\ {0.71}\right)}\)

Here population proportion is not mention in this interval so

The correct option is

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

Step 2

We are \(\displaystyle{82}\%\) to \(\displaystyle{98}\%\) confident \(\displaystyle{63}\%\) of adults in the country during the period of economic uncertainty felt wages paid to workers in industry were too low.

The correct option is

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

Step 3

We are \(\displaystyle{90}\%\) confident that the interval from 0.55 to 0.71 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.

The correct option is

A) The interpretation is reasonable.

Step 4

In \(\displaystyle{90}\%\) 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 0.55 and 0.71.

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