Chapter 8.1, Problem 6E

(a)

To determine

To Explain: the confidence interval

Explanation of Solution

Given:

95% confidence interval for the population proportion is given by (0.56, 0.62)

According to the given interval (0.56, 0.62) for 95% confidence interval, it means assuring 95% that proportion of U.S. adults who wish to lose weight so 95% of the proportion parameter will be lie between these two intervals and which is not come in these range then the proportion of U.S. adults who not wish to lose weight 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 (0.56, 0.62)

Formula used:

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

Calculation:

  $\begin{array}{c}\stackrel{⌢}{p}=\frac{0.56+0.62}{2}\\ =0.59\end{array}$

  $\begin{array}{c}\text{ME=}\frac{0.62-0.56}{2}\\ =0.03\end{array}$

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 (0.56, 0.62) will be 0.59

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 confidence interval

Answer to Problem 6E

Convincing evidence

Explanation of Solution

95% confidence interval for the population proportion is given by (0.56, 0.62) it means assuring 95% that proportion of U.S. adults who wish to lose weight. Observing that it is not likely that the population proportion who wants to lose weight is 0.50 so there is convincing evidence that more than half of the U.S. adults who want to lose weight.