Chapter 9.1, Problem 9.16E

a)

To determine

To find the 95% confidence interval for p

Answer to Problem 9.16E

The 95% confidence interval is, (0.56,0.62)

Explanation of Solution

Given:

C=confidence level = 0.95

Sample proportion:

  $\widehat{p}=59\%=0.59$

Margin of error = E = 3% = 0.03

Formula:

Confidence interval for population proportion is,

  $CI=\widehat{p}\mp E$

Calculation:

  $\begin{array}{l}\widehat{p}-E=0.59-0.03=0.56\\ \widehat{p}+E=0.59+0.03=0.62\end{array}$

b)

To determine

To explain why we can't just say that 59% of all adults want to lose weight.

Explanation of Solution

The given proportion 59% in the Gallup Poll is just an estimate of the true population proportion. Therefore, it is likely that the proportion of adults who want to lose weight deviates from the result of 59% of the Gallup Poll.

c)

To determine

To explain meaning of 95% confidence interval.

Explanation of Solution

We are 95% confidence that the true proportion of adults who want to lose weight will fall within the interval (0.56,0.62)

d)

To determine

To explain non sampling errors.

Explanation of Solution

We need to know about the non-sampling error. There are two non-sampling errors.

a)Response bias: In this type, the method can give different value from true value. That is, the respondent influenced to answer in a wrong way so that the result will bias.

b)Nonresponse bias: In this type the results of not having data for everybody in the sample.