# If we were researching some aspect of a population, and the sample proportion is 25% with a...

## Question:

If we were researching some aspect of a population, and the sample proportion is {eq}25\% {/eq} with a margin of error of {eq}4\% {/eq} at the {eq}95\% {/eq} confidence level. Does this mean that there is {eq}95\% {/eq} chance that the population proportion is between {eq}21\% {/eq} and {eq}29\% {/eq}? Why or why not? Explain.

## Confidence Interval for a Proportion:

Confidence interval gives upper and lower bounds true population proportion is most likely to be contained at a stated level of confidence. The width of the confidence interval is determined by sample size, sample variability and level of confidence.

The answer is no. The 95% confidence interval for the population proportion doesn't mean that population proportion will be contained between 21% and 29%. It means that, if 100 confidence intervals are constructed under the same conditions, 95 of the 100 confidence intervals will contain true population proportion. It can also be interpreted as, we are 95% confident that true population proportion will be contained between 21% and 29%. 