Confidence Interval for a Population Mean: Learn It 2

  • Check the assumptions for a one-sample [latex]t[/latex] confidence interval for population mean.
  • Calculate a confidence interval for a population mean and explain what it means.

Confidence Interval for a Population Mean

Confidence interval can be calculated using: estimate [latex]\pm[/latex] margin of error.

The margin of error is calculated a little differently: Instead of multiplying the value of the standard error by a value from the normal distribution, it is multiplied by a value from the appropriate [latex]t[/latex]-distribution.

confidence interval for a population mean

The formula for a confidence interval for a population mean is:

[latex]\bar{x} \pm (t\text{-critical value})\frac{s}{\sqrt{n}}[/latex]

 

The [latex]t[/latex]-critical value in the confidence interval will depend on the sample size (degrees of freedom for the [latex]t[/latex]-distribution: [latex]df=n-1[/latex]) and the confidence level.

 

This interval is often called a one-sample [latex]t[/latex] interval.

Let’s utilize technology to help us find the confidence interval for a population mean. 
Step 1: Under Enter Data, select Summary Statistics.
Step 2: Enter the Name of Variable, Sample Size, Sample Mean, and Sample Std. Dev. accordingly.
Step 3: Adjust the Confidence Level based on your question.

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