The relationship between the power of a statistical test

Question

1.According to the central limit theorem, a population which is skewed to begin with will still be skewed when it is re-formed as a distribution of sample means. 

• True
• False

2. How does variability in the distribution of sample means compare to variability in a population based on individual scores?

• Samples tend to vary less than individual scores.
• Samples exaggerate differences among scores.
• Individual scores tend to be more stable over time than samples.
• Sample means vary less than individual scores.

3. Which of the following is a provision of the central limit theorem?

• A skewed distribution will remain skewed however it is plotted.
• There are limits to the range of scores that can be fitted to a distribution.
• A distribution based on sample means will be normal.
• There will always be theoretical differences between distributions.

4. The desired sample size depends only the size of the population to be tested.

• True
• False

5. The z- test requires an estimate of the population standard deviation.

• True
• False

6. The one-sample t-test differs from the z-test in which way?

@Answer found in section 4.3 The One-sample t-Test, in Statistics for Managers

• There are no parameter values involved in a t-test.
• The t-test is more sensitive to minor differences between sample and population.
• With the t-test one can be confident of the normality of the data.
• The t-test requires no parameter standard error of the mean.

7. The desired sample size depends only the size of the population to be tested. (Points : 1)

• True
• False

8. What is the alternate hypothesis in a problem where sales group two is predicted to be ". . . significantly less productive than sales group one?"

@Answer found in sections 4.3 The One-sample t-Test and 4.4 Hypothesis Testing, in Statistics for Managers
HA: μ1

• ≠ μ 2
• HA: μ 1= μ 2
• HA: μ 1> μ2
• HA: μ 1< μ 2

9. What is the probability of type II error when the null hypothesis is rejected?

@Answer found in section 4.3 The One-sample t-Test, in Statistics for Managers

• 0.5
• 0.05
• 0.025
• 0

10. What is the relationship between the power of a statistical test and decision errors?

@Answer found in section 4.3 The One-sample t-Test, in Statistics for Managers

• Powerful tests minimize the risk of decision errors.
• Powerful tests are more inclined to type II than type I errors.
• Powerful tests compensate for decision errors with stronger effect sizes.
• Powerful tests minimize type II errors.