Question

1. In testing a null hypothesis H0 versus an alternative Ha, H0 is ALWAYS rejected if

A. at least one sample observation falls in the non-rejection region.

B. the test statistic value is less than the critical value.

C. p-value ≥ α where α is the level of significance. 1

D. p-value < α where α is the level of significance.

2. In testing a null hypothesis H0 : µ = 0 vs H0 : µ > 0, suppose Z be a test statistic and z0 be the observed value of Z from the sample. At significance level α, let zα be the critical value. It was observed that z0 < zα. What would be your conclusion?

A. H0 is rejected since there is sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

B. H0 is accepted since there is sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

C. Failed to reject H0 since there isn’t sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

D. H0 is rejected since there isn’t sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

3. For a test H0 : µ = 0 vs H0 : µ 6= 0 with test statistic T and value of the test statistic 1.36, what would be the appropriate p-value?

A. P(T > 1.36) B. P(T < 1.36) C. 0.05 D. 2 ∗ P(T > 1.36)

4. A Type II error is

A. rejection of null hypothesis H0 when, in fact, it is false.

B. failing to reject of null hypothesis H0 when, in fact, it is false.

C. rejection of null hypothesis H0 when, in fact, it is true.

D. failing to reject of null hypothesis H0 when, in fact, it is true.

Answer 1

1. In testing a null hypothesis H0 versus an alternative Ha, H0 is ALWAYS rejected if

Ans. p-value < α where α is the level of significance.

2. In testing a null hypothesis H0 : µ = 0 vs Ha : µ > 0, suppose Z be a test statistic and z0 be the observed value of Z from the sample. At significance level α, let zα be the critical value. It was observed that z0 < zα. What would be your conclusion?

Ans. Failed to reject H0 since there isn’t sufficient sample evidence with level α that the true value of the population mean µ is greater than 0.

3. For a test H0 : µ = 0 vs Ha : µ 0 with test statistic T and value of the test statistic 1.36, what would be the appropriate p-value?

Ans. 2 ∗ P(T > 1.36)

4. A Type II error is

Ans. failing to reject of null hypothesis H0 when, in fact, it is false.