9.6: Skills Focus: Selecting an Appropriate Inference Procedure
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.
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”.
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:
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.
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:
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.