Chapter 9.1, Problem 9.6E

a)

To determine

To find the parameter p.

Answer to Problem 9.6E

Population proportion is the proportion of adults in the population who think that deaths from guns would increase.

Explanation of Solution

Given:

The Harris Poll asked a sample of 1009 adults which causes of death they thought would become more common in the future. Gun violence topped the list: 706 members of the sample thought deaths from guns would increase. Although the samples in national polls are not SRSs, they are close enough that our method gives approximately correct confidence intervals.

Explanation:

In above study, let us assume that,

  $x$ =Number of members of the sample thought deaths from guns would increase = 706

n = Total number of adults = 1009

Here, population proportion is the proportion of adults in the population who think that deaths from guns would increase.

b)

To determine

To find the 95% confidence interval for p

Answer to Problem 9.6E

The 95% confidence interval is, (0.671 , 0.728)

Explanation of Solution

Given:

  $x$ =Number of members of the sample thought deaths from guns would increase = 706

n = Total number of adults = 1009

Formula:

Sample proportion:

  $\widehat{p}=\frac{x}{n}$

Confidence interval for population proportion is,

  $CI=\widehat{p}\mp Zc\sqrt{\frac{\widehat{p}(1-\widehat{p})}{n}}$

Calculation:

Sample proportion,

  $\widehat{p}=\frac{706}{1009}=0.7$

Now need to find Zc

The level of significance is = a =0.05

Therefore, Zc = Z _a/2 = 1.96 ..Using standard normal table

Therefore, the 95% confidence interval for population proportion is,

  $\begin{array}{l}\left(0.7-1.96\sqrt{\frac{0.7(1-0.7)}{1009}},0.7+1.96\sqrt{\frac{0.7(1-0.7)}{1009}}\right)\\ \left(0.671,0.728\right)\end{array}$

c)

To determine

To explain a margin of error of plus or minus 3 percentage points for this poll result.

Explanation of Solution

Given:

The 95% confidence interval is, (0.671, 0.728)

Explanation:

Agree with the margin of error.

We are 95% confidence that the proportion of adults in the population who think that deaths from guns would increase is between 0.671 and 0.728