# With 80% confidence, for sample portion 0.42 and sample size 25, what is the upper confidence...

## Question:

With {eq}80 \% {/eq} confidence, for sample portion {eq}0.42 {/eq} and sample size {eq}25 {/eq}, what is the upper confidence limit with {eq}2 {/eq} decimal places?

## Confidence limits

The confidence interval can be defined as the interval of values calculated for the sample data that will contain the true population parameter with a given degree of confidence. The most common level of confidence used is 95%.

## Answer and Explanation:

• Sample Size (n) = 25
• Sample proportion {eq}\left( {\hat p} \right) = 0.42 {/eq}

The z-critical value had been obtained from the z-table at the significance level of 0.20.

{eq}P\left( {z < 1.282} \right) = 0.20 {/eq}

The upper confidence limit is given as:

{eq}\begin{align*} &=\hat p + {z^*}\sqrt {\dfrac{{\hat p\left( {1 - \hat p} \right)}}{n}} \\ &= 0.42 + 1.282 \times \sqrt {\dfrac{{0.42\left( {1 - 0.42} \right)}}{{25}}} \\ & = 0.55 \end{align*} {/eq}

Hence, the 80% upper confidence limit is 0.55.