# With 80% confidence, for sample proportion 0.40 and sample size 24, what is the upper confidence...

## Question:

With {eq}80\% {/eq} confidence, for sample proportion 0.40 and sample size 24, what is the upper confidence limit with 2 decimal places?

## Confidence Interval for a Proportion:

Confidence interval gives a range of sample proportions likely to be true population proportion at a stated level of confidence. Confidence interval can be two sided or one sided.

Given that;

{eq}\hat p=0.40\\n=24 {/eq}

Use equation below to calculate upper confidence limit (UCL):

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

Find critical value z that corresponds to 80% level of confidence:

{eq}\displaystyle \frac{\alpha}{2}=\frac{1-0.80}{2}=0.10\\z_{0.10}=1.28 {/eq}

Plug in values into the formula above and calculate the UCL:

{eq}\begin{align*} \displaystyle UCL&=0.40+1.28\times \sqrt{\frac{0.40(1-0.40)}{24}}\\&=0.40+0.13\\&=0.53 \end{align*} {/eq}