3 min read•june 5, 2020

Josh Argo

Now that we have checked out conditions for inference, we can calculate the two aspects that are necessary for a significance test: our test statistics and p-value.

The first and necessary aspect of our calculations is calculating our t-score. Since we are dealing with quantitative data (means), we need to find our degrees of freedom first.

- When calculating by hand, we will take the smaller of the two samples and subtract 1. This is the same as we did in Unit 7.5 with 1 sample.
- When performing the test with technology such as a graphing calculator, the degrees of freedom will be given with the output.

To calculate our critical value, we used the typical formula:

To make it more specific for a t-score with the difference of two population means, our formula simplifies to:

This can be found on the Formula Sheet by simplifying the given formulas.

Now that we know our appropriate degrees of freedom and our t-score, we can refer to our Formula Sheet and refer to the appropriate row for our df. Looking across the tow, find the t-score value that is closest to the one you calculated for the t-score. Use the tail probability that most closely coordinates to your t-score.

A more exact way of calculating the p-value is to perform a 2 sample t-test in some form of technology such as a graphing calculator. As with any t-procedure, you are given the option of typing in the statistical information or entering in the data in list 1.

Once you enter the test in, the output gives you the t-score, df and p-value for your test. **On the AP test, it is essential that you write down ALL 3 of these on your response to receive full credit.**

For our green bean example from Unit 7.8, this is what our input would look like:

And our output would be as follows:

Now that you have the numbers you need, you can check the statistical claim of the null hypothesis.

As with any significance test, we are checking to see if our p is lower than the significance level. If our p is low, we reject the null with convincing evidence of the alternate hypothesis. If the p is not lower than the significance level, we fail to reject the null hypothesis.

Once you make your decision, you should be able to see if in fact there is a difference in your two populations.

For our green bean example, our conclusion would be as follows:

Since our p value is essentially 0 and less than 0.05, we reject our Ho. We have convincing evidence that the true mean number of green beans picked from Field A differs from that picked in Field B.

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