# 4.2.2 - Applying Confidence Intervals

4.2.2 - Applying Confidence Intervals

A 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.

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