Paired Samples T-Test on Calculator

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Paired Samples T-Test on Calculator, A paired samples t-test is an essential statistical method for comparing the means of two related groups.

This type of analysis is particularly useful when each observation in one sample corresponds to an observation in another sample.

Paired Samples T-Test on Calculator

One common application of the paired t-test is to assess the impact of an intervention on a dependent variable, such as measuring the differences in miles per gallon (mpg) for cars before and after applying a new fuel treatment.

In this article, we’ll guide you through conducting a paired samples t-test using a TI-84 calculator.

Example Scenario: Evaluating a New Fuel Treatment

Researchers are curious to understand whether a new fuel treatment has any effect on the average mpg of cars.

To investigate this, they decide to measure the mpg of 11 cars twice – once without the fuel treatment (control group) and once with it (treatment group).

Since each car serves as its own control, this study is an ideal candidate for a paired samples t-test.

Step-by-Step Guide to Conducting a Paired T-Test on a TI-84 Calculator

Step 1: Input Your Data

Begin by entering your data into the TI-84 calculator:

Press the STAT button and select EDIT.
Enter the mpg values for the control group (without fuel treatment) into the first column, labeled L1.
In the second column, L2, input the mpg values for the treatment group (with fuel treatment).
Next, to calculate the differences between the two samples, move to the third column, L3. Highlight L3, then press 2nd and 1 (to select L1) followed by a minus sign, and then press 2nd and 2 (to select L2). Press ENTER, and the differences will automatically populate in L3 using the formula L1 – L2.

Step 2: Perform the Paired T-Test

Now, it’s time to conduct the paired t-test:

Press STAT, navigate to the TESTS menu, and scroll down to find 2:T-Test, then press ENTER.
You’ll be prompted to provide some information:

Inpt: Select Data for raw data input.
μ0: Enter the mean difference hypothesized under the null hypothesis, which is typically 0.
List: Input L3 (the list containing the differences). To do this, press 2nd and 3.
Freq: Leave this set to 1.
μ: Since this is a two-tailed test, highlight ≠μ0 and press ENTER.

Finally, navigate to Calculate and press ENTER to compute the results.

Step 3: Interpret the Results

Once the calculator has processed your input, it will display the test results. Here’s a breakdown of what to look out for:

μ ≠ 0: This indicates the alternative hypothesis of the test.
t = -1.8751: This is the t test statistic.
p = 0.0903: The corresponding p-value for the test statistic.
x = -1.5455: The mean difference between the two groups.
sx = 2.7336: The standard deviation of the differences.
n = 11: The total number of paired samples.

In our example, the p-value (0.0903) is greater than the common alpha level of 0.05.

Therefore, we fail to reject the null hypothesis, concluding that there isn’t sufficient evidence to state that the new fuel treatment significantly affects the average mpg of the cars tested.

Conclusion

Conducting a paired samples t-test on a TI-84 calculator is a straightforward process that can provide valuable insights, especially in experimental settings like our fuel treatment example.

With careful data input and interpretation, you can effectively assess the differences between paired samples and draw meaningful conclusions from your research.

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