When testing a hypothesis, why do not we set the probability of a Type I error to be extremely small?
Exercises for Section 9.1
CONCEPTS
9.1 Which hypothesis (the null hypothesis, H0, or the alternative hypothesis, Ha) is the “status quo” hypothesis (that is, the hypothesis that states that things are remaining “as is”)? Which hypothesis is the hypothesis that says that a “hoped for” or “suspected” condition exists?
9.2 Which hypothesis (H0 or Ha) is not rejected unless there is convincing sample evidence that it is false? Which hypothesis (H0 or Ha) will be accepted only if there is convincing sample evidence that it is true?
9.3 Define each of the following:
a Type I error
b Type II error
c α
d β
9.4 For each of the following situations, indicate whether an error has occurred and, if so, indicate what kind of error (Type I or Type II) has occurred.
a We do not reject H0 and H0 is true.
b We reject H0 and H0 is true.
c We do not reject H0 and H0 is false.
d We reject H0 and H0 is false.
9.5 If we reject H0, what is the only type of error that we could be making? Explain.
9.6 If we do not reject H0, what is the only type of error that we could be making? Explain.
9.7 When testing a hypothesis, why don’t we set the probability of a Type I error to be extremely small? Explain.