Parsons Clark
03/29/2023 · High School
Confidence Intervals - Proportions An interactive poll found that 347 of 2,394 adults aged 18 or older have at least one tattoo. (a) Obtain a point estimate for the proportion of adults who have at least one tattoo. (b) Construct a \( 95 \% \) confidence interval for the proportion of adults with at least one tattoo. (c) Construct a \( 99 \% \) confidence interval for the proportion of adults with at least one tattoo. (d) What is the effect of increasing the level of confidence on the width of the interval?
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(a) Point Estimate: \( \frac{347}{2394} \)
(b) \( 95\% \) Confidence Interval: \( \text{Point Estimate} \pm 1.96 \times \sqrt{\frac{\text{Point Estimate} \times (1 - \text{Point Estimate})}{\text{Total Number of Adults}}} \)
(c) \( 99\% \) Confidence Interval: \( \text{Point Estimate} \pm 2.576 \times \sqrt{\frac{\text{Point Estimate} \times (1 - \text{Point Estimate})}{\text{Total Number of Adults}}} \)
(d) Increasing confidence level increases the width of the interval.
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