Math 143 C/E, Spring 2001
IPS Reading Questions
Chapter 7, Section 1, Part 2: pp. 507-517 (“power of the
t test”)
and pp. 519 (“sign test”)-523
- In the blue box on p. 508 that summarizes the “One-Sample
t Test”, the authors say that the “P-values
are exact if the
population distribution is normal and are approximately correct
for large n in other cases.” Later in the section
(pp. 515-517) they expound on some of these “other cases”.
Describe these cases and indicate how large n should be
in each. Are there situations in which you should be wary of
the validity of a t procedure even for large n?
- Finish this sentence appropriately:
There is a strong relationship between the two inference
procedures: confidence intervals and hypothesis tests. Specifically,
when a sample mean is used to determine a level C confidence
interval, the result of a two-sided hypothesis test for null
hypothesis H0: m = m0 will generally be significant at the
a = 1 - C level whenever ...
- How do matched pairs inference procedures differ from
those we have learned so far?
- Example 7.12 demonstrates a sign test-approach for a matched pairs
experiment. Notice how the quantitative data (scores and difference
in scores) is considered categorically (either a person did better
after special training or did not), the count of those doing better
after training has a binomial distribution, and the null hypothesis
is that the probability of success due to the training is p
= 1/2. Under what circumstances would it be better to use
such a test than a matched-pairs t test?