*To calculate a confidence interval on the TI-84, enter your data in a list, go to STAT, arrow over to TESTS, arrow down to Interval, enter your confidence level, the list where your data is stored, and the population mean if known. The calculator will provide the lower and upper bounds of the confidence interval.*

## Introduction

In statistics, a confidence interval gives a range of plausible values for an unknown population parameter based on a sample of data. The confidence interval is constructed using the sample data so that the probability the interval contains the actual population parameter is equal to the confidence level. A common example is calculating a 95% confidence interval for the population mean based on a sample mean.

Confidence intervals provide valuable information from samples. Rather than providing a single point estimate, the interval gives a measure of precision and accounts for sampling variability. In practical terms, we can say there is a 95% probability the population mean lies within the 95% confidence interval computed from a sample.

Being able to calculate confidence intervals easily is important for many fields like science, psychology, and business. With some simple steps, you can use the TI-84 graphing calculator to quickly find confidence intervals for means and proportions. In this blog post, we’ll go through the process step-by-step.

## Understanding Confidence Level and Margin of Error

The confidence level, typically expressed as a percentage like 95%, gives the probability that the confidence interval captures the true population parameter. Generally, 95% and 99% confidence levels are commonly used.

The margin of error indicates the precision of the estimate. A smaller margin of error due to a larger sample size produces a narrower confidence interval. The margin of error depends directly on the confidence level – higher confidence levels widen the interval.

On the TI-84, the margin of error formula is built into the confidence interval calculation. You specify the confidence level, and the calculator determines the corresponding margin of error.

## Entering Data into Lists

Before computing a confidence interval on the TI-84, you first need to enter your sample data into one of the calculator’s lists. Lists L1, L2, L3, and L4 are available to store data.

To enter data:

- Press STAT
- Select 1:Edit… to open the list editor
- Enter your data values into one of the lists
- Exit the list editor when done

Once your data is stored in a list, you are ready to calculate the confidence interval.

## Computing the Confidence Interval

Here are the step-by-step instructions to compute a confidence interval on the TI-84:

- Press STAT
- Arrow over to TESTS
- Arrow down to 8:Interval
- Enter the confidence level as a decimal (e.g. .95 for 95%)
- Enter the list where your data is stored
- If estimating the population mean, enter the hypothesized population mean or leave blank if unknown
- Press ENTER

The calculator will display the lower and upper bounds of the confidence interval along with some additional information. The values in the bottom row are the ones needed for the confidence interval.

## Interpreting and Using the Results

It is important to correctly interpret what the computed confidence interval represents. Remember that wider intervals indicate less precision, while narrower intervals reflect greater accuracy.

The confidence interval captures the range of plausible values for the population parameter based on the sample. We can say with 95% confidence that the true population mean lies between the lower and upper interval boundaries.

Confidence intervals are useful for more than just estimating means. The TI-84 can also generate intervals for population proportions and standard deviations. Having the ability to easily compute key statistics and confidence intervals is vital for analyzing and interpreting data.

## Conclusion

The TI-84 graphing calculator provides simple tools for generating confidence intervals. By entering your sample data into lists, specifying the confidence level, and indicating the appropriate parameters, you can easily find intervals for means, proportions, and other statistics. Confidence intervals give valuable insight into population parameters based on sample data.

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