One-Sample T-Test on TI-84 Calculator
One-Sample T-Test on TI-84 Calculator, Are you interested in determining whether the mean of a population is equal to a specific value?
If so, a one-sample t-test might be the perfect statistical tool for you!
One-Sample T-Test on TI-84 Calculator
This guide will walk you through the process of performing a one-sample t-test on a TI-84 calculator, providing a step-by-step example to help you along the way.
Understanding the One-Sample T-Test
The one-sample t-test is a statistical method used to test if the mean of a population differs from a specified value.
It’s particularly useful when you have a small sample size and do not know the population standard deviation.
Example Scenario: Testing Car Miles Per Gallon (MPG)
Imagine researchers are looking to find out if a specific type of car achieves an average of 20 miles per gallon (mpg).
They randomly sample 74 cars and discover that the mean mpg is 21.29, with a standard deviation of 5.78.
We will conduct a one-sample t-test to evaluate if the true mean mpg for this type of car significantly differs from 20 mpg.
Step-By-Step Instructions for the TI-84 Calculator
Step 1: Access the T-Test Function
- Turn on your TI-84 calculator.
- Press the STAT button.
- Scroll over to the TESTS tab.
- Find and select T-Test by pressing ENTER.
Step 2: Input the Necessary Information
Your calculator will prompt you for specific inputs:
- Input Method: Choose Stats since we are working with summary statistics.
- μ0: Enter the hypothesized mean (the value in the null hypothesis). For our example, enter 20.
- x̄: Enter the sample mean. We will input 21.29.
- sx: Enter the sample standard deviation. Input 5.78.
- n: Enter the sample size. In this case, input 74.
- μ: Select the alternative hypothesis. Since we are conducting a two-tailed test (to see if the mean is not equal to 20), select ≠μ0.
- Finally, highlight Calculate and press ENTER.
Step 3: Interpret the Results
Upon completion, your calculator will display results for the one-sample t-test:
- Alternative Hypothesis (μ≠20): The hypothesis we are testing against.
- t=1.9199: This is the calculated t-test statistic.
- p=0.0588: This is the p-value corresponding to the t-test statistic.
- Sample Mean (x̄=21.29): This is the mean mpg from our sample.
- Sample Standard Deviation (sx=5.78): The standard deviation entered into the calculator.
- Sample Size (n=74): The number of cars in the sample.
Conclusion of the Test
In our example, the p-value (0.0588) is greater than the common significance level of 0.05.
This indicates that we fail to reject the null hypothesis, suggesting that there isn’t sufficient evidence to conclude that the true mean mpg for this type of car is different from 20 mpg.
Final Thoughts
Conducting a one-sample t-test on the TI-84 calculator is straightforward with this step-by-step guide.
By inputting your data correctly and interpreting the results accurately, you can effectively analyze whether your sample mean significantly differs from a specific population mean.
Keep practicing, and you’ll master this statistical test in no time!
