Chapter 8.1, Problem 5E

(a)

To determine

To Explain: the confidence interval

Explanation of Solution

Given:

95% confidence interval for the population proportion is given by (0.63, 0.69)

According to the given interval (0.63, 0.69) for 95% confidence interval, it means assuring 95% that proportion of U.S. adults who favouring like amendment is lies between two ranges 0.63 and 0.69 and which is not come in these range then the proportion of U.S. adults who not favouring amendment will come in this range

(b)

To determine

To Explain: the point estimation and margin of error

Explanation of Solution

Given:

95% confidence interval for the population proportion is given by (0.63, 0.69)

Formula used:

  $\begin{array}{c}\stackrel{⌢}{p}=\frac{\text{UCL+LCL}}{2}\\ \text{ME}=\frac{\text{UCL-LCL}}{2}\end{array}$

Calculation:

  $\begin{array}{c}\stackrel{⌢}{p}=\frac{0.63+0.69}{2}\\ =0.66\end{array}$

  $\begin{array}{c}\text{ME=}\frac{0.69-0.63}{2}\\ =0.03\end{array}$

Point estimation

It lies absolutely in the halfway of the confidence interval therefore the point estimate is then the average of the boundaries of the interval. Here point estimation of the interval of (0.63, 0.69) will be 0.66

Margin of error

Margin of error is half of the difference of confidence interval. Here margin of error of the interval of (0.63, 0.69) will be 0.03

(c)

To determine

To Explain: the claim on the basis of the interval

Answer to Problem 5E

Not convincing evidence

Explanation of Solution

95% confidence interval for the population proportion is given by (0.63, 0.69) , it means assuring 95% that proportion of U.S. adults who favouring like amendment is lies between two ranges 0.63 and 0.69. Observing that the confidence interval contains $\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ or 0.67, which is indicating that it is likely that 0.67 of U. S. Adults favouring such an amendment

There is no convincing evidence of 0.67 of U. S. Adults favour such an amendment