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in a survey 420 U.S. females ages 18 to 64, 279 say they have gone to the dentist in the past year. Construct a 90% confidence interval for the population proportion.

in a survey 420 U.S. females ages 18 to 64, 279 say they have gone to the dentist-example-1
User Refael Sheinker
by
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1 Answer

13 votes
13 votes

The formula to calculate the confidence interval is


P\pm z*\sqrt[]{(P(1-P))/(n)}

Where


\begin{gathered} P=\text{ sample proportion} \\ n=sample\text{ size} \\ z=\text{ z-score} \end{gathered}

We can calculate the sample proportion by


\begin{gathered} P=(x)/(n) \\ \text{Where x is the successes} \end{gathered}

The parameters are


\begin{gathered} x=279 \\ n=420 \\ \end{gathered}

Using an online calculator, the z-score for a 90% confidence interval is 1.645.

Therefore, we can calculate P to be:


P=(279)/(420)=0.6643

Hence, we can calculate calculate the confidence interval by substituting the values


\begin{gathered} =0.6643\pm1.645\sqrt[]{(0.6643(1-0.6643))/(420)} \\ =0.6643\pm1.645(0.023) \\ =0.6643\pm0.0378 \end{gathered}

Therefore, the lower limit of the confidence interval is


\begin{gathered} =1.645-0.0378 \\ =1.6072 \end{gathered}

The lower limit of the confidence interval is 1.6072

Therefore, the upper limit of the confidence interval is


\begin{gathered} =1.645+0.0378 \\ =1.6828 \end{gathered}

Therefore, the upper limit of the confidence interval is 1.6828

User Chen Xing
by
2.7k points
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