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The Harris Poll conducted a survey in which they asked, "How many tattoos do you currently have...

Question:

The Harris Poll conducted a survey in which they asked, "How many tattoos do you currently have on your body?" Of the {eq}1205 {/eq} males surveyed, {eq}181 {/eq} responded that they had at least one tattoo. Of the {eq}1097 {/eq} females surveyed, {eq}143 {/eq} responded that they had at least one tattoo. Construct a {eq}95\% {/eq} confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Confidence Interval:

The confidence interval for the difference between the population proportion is constructed by the normal distribution. The confidence coefficient of the normal distribution is calculated by the excel function, NORMINV().

Answer and Explanation:

Males:

Sample size, {eq}n_1 = 1205 {/eq}

Sample proportion, {eq}\hat{p}_1 = \dfrac{181}{1205} = 0.150 {/eq}


Females:

Sample size, {eq}n_2 = 1097 {/eq}

Sample proportion, {eq}\hat{p}_2 = \dfrac{143}{1097} = 0.130 {/eq}


The 95% confidence interval for the difference between the population proportions is defined as:

{eq}\hat{p}_1 - \hat{p}_2 \pm z_{0.05/2}\times \sqrt{\dfrac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \dfrac{\hat{p}_2(1-\hat{p}_2)}{n_2}} {/eq}


Excel function for the confidence coefficient:

=NORMINV(0.05/2,0,1)


{eq}0.15 - 0.13 \pm 1.96\times \sqrt{\dfrac{0.15(1-0.15)}{1205} + \dfrac{0.13(1-0.13)}{1097}}\\ (-0.0083, \ 0.0483) {/eq}


Learn more about this topic:

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Finding Confidence Intervals for Proportions: Formula & Example

from Statistics 101: Principles of Statistics

Chapter 9 / Lesson 8
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