# Calculate the confidence interval (Statistics problem)

• RedonYellow
In summary, the conversation is about calculating the confidence interval for a problem using a T-84 calculator. The person is having trouble getting the correct answer and asks for help. They mention the equations they are using and the data they input into the calculator. They also mention a possible issue with the z values. They suggest checking what 2 sample standard deviations from the sample mean would give as a solution.
RedonYellow
I am trying to calculate the confidence interval for this problem using my T-84, and it's driving me mad because I'm so close to the correct answer. The problem is

## Homework Statement

The answer to this problem is (22769.83, 30059.41) (This is an example problem.) When I try to duplicate this in my calculator, my answer is (22772,30058).

## Homework Equations

I go to STAT>TESTS>7>STATS

## The Attempt at a Solution

I put the data in like this
standard deviation: 8150
mean: 26414.62
n: 20
C-Level: 0.9544

Could someone tell me what I'm doing incorrectly, please.

I'm not familiar with your calculator but my guess is some problem with the Z values. If you check you will see that 95.44% corresponds to a right and left tail are each of .0228 which in turn gives a z value of 2. Why don't you just check what 2 sample standard deviations from the sample mean get you?

## What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. It is used to estimate the true value of a population based on a sample of data.

## How do you calculate a confidence interval?

A confidence interval is calculated using the formula: sample statistic ± margin of error. The margin of error is determined by the confidence level, sample size, and standard deviation of the sample.

## What is the significance of the confidence level?

The confidence level represents the probability that the true population parameter falls within the calculated confidence interval. For example, a confidence level of 95% means that there is a 95% chance that the true population parameter lies within the calculated interval.

## What factors can affect the width of a confidence interval?

The width of a confidence interval can be affected by several factors, including the confidence level, sample size, and standard deviation of the sample. A wider interval means a lower level of confidence, a smaller sample size, or a higher standard deviation.

## Why is it important to calculate a confidence interval?

Calculating a confidence interval allows us to estimate the true value of a population parameter and determine how confident we can be in that estimate. It also helps us to assess the precision of our sample data and make informed decisions based on the results.

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