1. Using and Finding “Student’s t”
AP Statistics
Using and Finding “Student’s t”

2. Finding Critical Values using a Calculator
Find the DISTR (2nd VARS)
Remember invNorm? Well, now look for invT ** If you have a TI-83 then you need to come see me. You do not have this on yours
You will need to specify the percentile you are looking for AND the df
For example: if we have 6 degrees of freedom and we want to make a 95% CI
invT(.975,6) will be what we enter

3. Finding Probabilities using a Calculator
Find the DISTR (2nd VARS)
Remember normalcdf? We are now looking for tcdf
Let’s use a t of with 12 degrees of freedom
Enter (1.645,99,12)
What do you get?
Did you get ?

4. Using t tables and your calculator, estimate:
The Critical value is 1.740
the critical value of t for a 90% confidence interval with df=17
Do you get ?

5. Using t tables and your calculator, estimate:
the critical value of t for a 98% confidence interval with df=88
The Critical value is 2.37
Did you get

6. Using t tables and your calculator, estimate:
The P-value is
the P-value for t≥2.09 with 4 degrees of freedom

7. Using t tables and your calculator, estimate:
the P-value for the absolute value of t is greater than with 22 degrees of freedom
The P-value is

8. Using t tables and your calculator, estimate:
the critical value of t for a 95% confidence interval with df=7
The critical value is 2.36

9. Using t tables and your calculator, estimate:
the critical value of t for a 99% confidence interval with df=102
The critical value is 2.62

10. Using t tables and your calculator, estimate:
the P-value for t≤2.19 with 41 degrees of freedom
The P-value is

11. Using t tables and your calculator, estimate:
the P-value for the absolute value of t is greater than 2.33 with 12 degrees of freedom
The P-value is

12. Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
The shape becomes closer to Normal, the center does not change, and the spread becomes narrower.

13. The Critical value becomes smaller, approaching 1.96
Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
The Critical value becomes smaller, approaching 1.96