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With 80% confidence, for a sample proportion of 0.40 and sample size 29, what is the upper...

Question:

With 80% confidence, for a sample proportion of 0.40 and sample size 29, what is the upper confidence limit with with 2 decimal places?

Confidence Interval for a Proportion:

Confidence interval gives upper and lower bounds true population proportion is most likely to lie at stated level of confidence. Confidence interval can be one sided or two sided.

Answer and Explanation:

The upper confidence bound (UCB) is calculated using the equation below:

{eq}\displaystyle UCB=\hat p+z_{\frac{\alpha}{2}}\sqrt{\frac{p(1-p)}{n}} {/eq}

The critical value z that corresponds to 80% confidence interval is 1.28. Use the P-hat as unbiased estimator of population proportion to calculate the UCB:

{eq}\begin{align*} \displaystyle UCB&=0.40+1.28\times \sqrt{\frac{0.4(1-0.4)}{29}}\\&=0.40+0.12\\&=0.52 \end{align*} {/eq}

The upper confidence limit is 0.52.


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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