In a survey of 2085 adults in a certain country conducted during a period of eco

Rivka Thorpe 2021-09-23 Answered
In a survey of 2085 adults in a certain country conducted during a period of economic?
Uncertainty, \(\displaystyle{63}\%\) thought that wages paid to workers in industry were too low. The margin of error was 8 percentage points with \(\displaystyle{90}\%\) confidence.
For parts (1) through (4) below, which represent a reasonable interpretation of the survey results. For those that are not reasonable, explain the flaw.
1) 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.
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 sugguests that this interbal 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.
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. 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 sugguests that this interbal 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.
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.
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 sugguests that this interbal 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.
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.
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 sugguests that this interbal 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.

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Expert Answer

un4t5o4v
Answered 2021-09-24 Author has 13902 answers
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.
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