# Confidence Interval: Definition

The other way of looking at or using CI's is to estimate the mean of the population from the mean of a sample. First we conjectured a mean for the population, e.g., here it was 100. Then we went through the rest of the steps of the procedure and obtained a CI that was set up around the sample's mean. We had 95% confidence that the mean of the population would be found in this interval. We backed off this position when we realized that we could draw several different samples and come up with several different CI's. The mean of the population could be declared most any number.

## What is the difference between confidence intervals and hypothesis ..

### confidence intervals and hypothesis ..

Historically, Hypothesis Testing was the first tool ofstatistical inference that was created to answer questions like "does thisgrowing method improve the yield of cotton?", or "are babies lesslikely to have a particular disease if we know the health of theirparents?" Confidence Interval, on the other hand, was invented later, andit was used in situations where people don't necessary want a "yes"or "no" answer.

### Confidence Interval & Hypothesis Testing of Proportion

In this graph, the REFLINE statement is used to display (in red) the observed value of the statistic for the original data. A second REFLINE statement plots (in blue) an approximate 95% confidence interval for the skewness parameter, which is computed in the next section. The bootstrap confidence interval contains 0, thus you cannot conclude that the skewness parameter is significantly different from 0.

## Confidence Interval and Hypothesis Test for a Proportion

As it turns out, there are a couple of ways of looking at confidence intervals. CI's have different meanings depending upon whether they are used in hypothesis testing (as above) or in parameter estimation such as estimating a population mean. Since we already looked at hypothesis testing, the following is an example of parameter estimation.

## Comparison Confidence Interval and Hypothesis Testing

Recall that **confidence intervals **measure uncertainty of an estimate.

The asymptotic normality of the ML estimate, which gives the approximation