Question

1. Regarding a two-tailed z-test with an alpha of 0.05, we would need a Zobt with an absolute value less than 1.96 in order to reject the null hypothesis.

True or False?

2. What happens to the probability of committing a Type I error if the level of significance is changed from α = 0.05 to α = 0.01?

A. It increases

B. It decreases

C. It stays the same

D. Cannot determine

3. Given a Zobt of -1.99 , an alpha of 0.05, an alternative hypothesis of μ ≠ 100, and a null hypothesis of μ = 100,  which of the following conclusions can be made?

A. The sample mean significantly differs from the population mean of 100.

B. We should reject the null hypothesis

C. The sample mean did NOT significantly differ from the population mean of 100.

D. The first two conclusions are true.

4. A one-tailed z-test with an alpha of 0.01 produces a significant result. Which of the following Zobt is the most likely to have been associated with the sample mean?

A. -2.35

B. -1.99

C. 1.70

D. 2.15

Answer 1

1. True

2. B. It decreases

3. The observed value of the test statistic

and critical value

Since , so we reject H₀ at 5% level of significance.

ans-> B. We should reject the null hypothesis

4. At an alpha of 0.01 and for a one tailed test, z critical can be either 2.32635 or -2.32635

ans-> A. -2.35