Question

True or False

1. Hypothesis tests are robust to the significance level you choose, meaning regardless of the alpha level: .10, .05, or .01, our test will have the same conclusion or result.

2. If alpha is greater than the p-value, then we reject the null hypothesis.

3. The p-value is strictly the probability the null hypothesis being true.

4. Hypothesis tests are accessing the evidence provided by the data and deciding between two competing hypotheses about the population parameter.

5. When the alternative hypothesis is saying that the parameter is different than the hypothesized value, we have a two-sided test.

Answer 1

1. False. For example, for n=30 and population standard deviation is unknown, some time we use large sample test i.e. Z test instead of t test when our parameter of interest is population mean. In that situation, we can get different conclusions for given alpha. This is also observed in other large sample and exact tests. Moreover this scenario is also found in non parametric tests (for example sign test and Wilcoxon sign rank test).

2. True.

3. False, since p-value is the probability of obtaining results as extreme as the observed results of a statistical hypothesis test, when the null hypothesis is true.

4. True.

5. True.