PROBLEM #1:
For each of the following statements, determine whether it is true or false. Label "T" if it is true, otherwise label "F".
a. The null hypothesis is the claim that is initially assumed to be true while the alternative hypothesis is the assertion that is contradictory to the null hypothesis. They are two competing hypotheses.
b. Depending on the form of the alternative hypothesis, we have three different forms of hypothesis tests, namely, upper-tailed, lower-tailed, and two-tailed tests.
c. A test statistic and a rejection region are two basic ingredients of a hypothesis test.
d. For a hypothesis test, we have two results: rejecting H0 and failing to reject H0.
e. P-value is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.
f. For a hypothesis test, if the calculated P-value is less than or equal to the specified significance level, we should reject the null hypothesis.
g. In a hypothesis test, Type I error is the error made when the null hypothesis is rejected when in fact the null hypothesis is true; Type II error is the error made when the null hypothesis is not rejected when it is false.
h. For a hypothesis test regarding the population mean, we should use t-test if the underlying distribution of the observations is normal, the sample size is not large enough, and the population variance is unknown. However, if we know the population variance, we should use z-test.
i. For a z-test regarding the population mean, if Ha : μ > μ0 is the alternative hypothesis, then the rejection region should be z ≥ zα where zα is the z critical value associated with the significance level α.
j. For a t-test regarding the population mean, if Ha : μ > μ0 is the alternative hypothesis, then the rejection region should be t > tα,n−1 where tα,n−1 is the t critical value associated with the significance level α (suppose that the given sample is of size n).