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Q.11

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Found in: Page 482

### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

# Prayer in school A New York Times/CBS News Poll asked the question, “Do you favor an amendment to the Constitution that would permit organized prayer in public schools?” Sixty-six percent of the sample answered “Yes.” The article describing the poll says that it “is based on telephone interviews conducted from Sept. 13 to Sept. 18 with $1664$ adults around the United States, excluding Alaska and Hawaii. . . . The telephone numbers were formed by random digits, thus permitting access to both listed and unlisted residential numbers.” The article gives the margin of error for a $95%$ confidence level as $3$ percentage points.(a) Explain what the margin of error means to someone who knows little statistics. (b) State and interpret the 95% confidence interval. (c) Interpret the confidence level.

a). On average the sample proportion will be within $3%$ of the true proportion in 95% of all samples.

b). We are localid="1649754733996" $95%$ confident that the true population proportion is between localid="1649754744695" $0.63$ and localid="1649754756510" $0.69$.

c). On average, in localid="1649754767371" $95%$ of all samples the corresponding confidence interval will contain the true population proportion localid="1649754793252" $p$.

See the step by step solution

## Part (a) Step 1: Given Information

The article gives the margin of error for a $95%$ confidence level as $3$ percentage points.

## Part (a) Step 2: Explanation

The margin of error is the amount of error that is made, on average, in estimating the population proportion $p$ by the sample proportion $\stackrel{^}{p}$.

Thus on average the sample proportion will be within $3%$ of the true proportion in $95%$ of all samples.

## Part (b) Step 1: Given Information

The article gives the margin of error for a $95%$.

$\stackrel{^}{p}=66%=0.66$

$E=3%=0.03$

## Part (b) Step 2: Explanation

The boundaries of the confidence interval is the sample proportion increased/decreased by the margin of error:

$0.63=0.66-0.03=\stackrel{^}{p}-E

We are $95%$ confident that the true population proportion is between $0.63$ and $0.69$.

## Part (c) Step 1: Given Information

The article gives the margin of error for a $95%$ confidence level.

## Part (c) Step 2: Explanation

The confidence level is $95%$.

This means: On average, in $95%$ of all samples the corresponding confidence interval will contain the true population proportion $p$.