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.

Question

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.

Accepted Answer

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" $p$ .

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