2 min read•april 28, 2021

Josh Argo

One of the most important skills in AP Statistics is being able to identify the best inference procedure to use in order to complete a hypothesis test or confidence interval. We have covered all of the following types of procedures:

- One Proportion Z Test
- One Proportion Z Interval
- One Sample T Test
- One Sample T Interval
- Matched Pairs T Test
- Two Proportion Z Test
- Two Proportion Z Interval
- Two Sample T Test
- Two Sample T Interval
- Chi Squared Goodness of Fit Test
- Chi Squared Test for Independence
- Chi Squared Test for Homogeneity
- Linear Regression T Interval
- Linear Regression T Test

If given a problem involving one of the linear regression t procedures, it is most common that you will be given a computer output and be asked to make a conclusion or construct an interval.

**Example**

Here is a computer output similar to what you would see on the AP test. This is based on a study with a sample size of 30.

Remember from Unit 2, that we are only focusing on the inference values associated with the slope, which is the row entitled “Sick Days”.

**Confidence Interval**

In order to construct a confidence interval like we discussed in Section 9.2, we will need the point estimate (sample slope), t-score and standard error.

Everything except our t-score is given in the computer output, so we have to calculate our t-score based on our confidence level and sample size. We will first calculate our degrees of freedom of 28 and then use that with the invT function to calculate our t-score. We get a t-score of 2.05 for a 95% confidence level.

For the computer output above, our confidence interval would be:

0.962.05(0.12)

Which comes out to be (0.714, 1.206).

In this case, we can be sure that the two variables of interest (sick days and wellness visits) because 0 is not contained in our interval and therefore there is evidence that the two have some correlation. This is also supported by our high r value that could be easily computed by the R2 value.

**Hypothesis Test**

The other option for inference would be to use the p-value to make a judgment on the hypothesis test. In this example, our p-value for the slope is 0.02, which is usually considered significant enough to reject our null hypothesis.

In this instance, our conclusion would be:

- Since our p value 0.02<0.05, we reject the null hypothesis. We have significant evidence that the true slope of the regression model between the number of sick days taken and the number of wellness visits is not 0.

Again, since we have some evidence that the slope is not 0, this shows that these two things **are correlated, **which is also evidenced by the R2 and resulting correlation coefficient.

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