# 4.2.2 - Applying Confidence Intervals

4.2.2 - Applying Confidence IntervalsA confidence interval contains a range of acceptable estimates of the population parameter. Values in a confidence interval are reasonable estimates for the true population value. Values not in the confidence interval are not reasonable estimates for the population value.

## Example: Correlation Between Height and Weight

At the beginning of the Spring 2017 semester a sample of World Campus students were surveyed and asked for their height and weight. In the sample, Pearson's *r *= 0.487. A 95% confidence interval was computed of [0.410, 0.559].

**Research question: Is there convincing evidence of a positive correlation between height and weight in the population of all World Campus students?**

The entire confidence interval is greater than zero which means that all reasonable estimates of the population correlation are positive. Yes, there is convincing evidence of a positive correlation between height and weight in the population of all World Campus students.

## Example: Seatbelt Usage

A sample of 12th grade females was surveyed about their seatbelt usage. A 95% confidence interval for the proportion of all 12th grade females who always wear their seatbelt was computed to be [0.612, 0.668].

**Research question: Is there convincing evidence that the proportion of all 12th grade females who always wear their seatbelt is different from 0.65?**

The value of 0.65 is contained within our confidence interval. This means that 0.65 is a reasonable value of the population proportion. We cannot conclude that the population proportion is different from 0.65.

## Example: IQ Scores

A random sample of 50 students at one school was obtained and each selected student was given an IQ test. These data were used to construct a 95% confidence interval of [96.656, 106.422].

**Research question: Is there convincing evidence that the mean IQ score at this school is different from the known national average of 100?**

The 95% confidence interval contains 100. This means that 100 is a reasonable estimate for the mean IQ score of students at this school. There is not enough evidence that the mean at this school is different from 100.