Hypothesis, Interval, Questions Ch4 Test Questions & Answers

Chapter 4

True and False Questions:

1. True or False: Statistical tools allow us to prove the null hypothesis is wrong.
2. True or False: Type I errors occur when we fail to reject a null hypothesis even when it is false.
3. True or False: Type II errors occur when we fail to reject a null hypothesis even when it is false.
4. True or False: In hypothesis testing, what we really care about is the size of the ₁ coefficient.
5. True or False: We fail to reject the null hypothesis if the test statistic is greater than the critical value.
6. True or False: A large sample will tend to produce high-power statistical tests while small samples will tend to produce low power statistical tests.

Multiple Choice Questions:

1. Reducing the significance level (alpha) will:
   1. Will increase the probability of making a Type I Error
   2. Will increase the probability of making a Type II Error
   3. Will not affect the probability of making either error
   4. Will decrease the probability of making a Type II Error
2. In which case would we choose to a one-sided alternative hypothesis over a two-sided alternative hypothesis?
   1. It does not matter what type of alternative hypothesis we specify.
   2. Choose a one sided alternative hypothesis when the theory and literature suggests either that the coefficient should be greater than zero or that the coefficient should be less than zero.
   3. We choose a one sided alternative hypothesis when we have a large sample size.
   4. We choose a one sided alternative hypothesis when we specify a low (0.01) alpha.
3. Assume that the two-sided 95% confidence interval for the effect of a price on amount of beef purchased is between 0.30 and 0.38. Which of the following statements is incorrect?
   1. We will reject the null hypothesis that this coefficient equals zero.
   2. There is less than a 2.5% chance that a coefficient higher than 0.38 would produce the coefficient we actually observe.
   3. There is a 95% chance that the true coefficient is between 0.30 and 0.38.
   4. There is a 95% chance that a random sample will produce a confidence interval that includes the true coefficient.
4. A null and alternative hypothesis are statements pertaining to:
   1. Sample parameters
   2. Sample statistics
   3. Population parameters
   4. It depends – In some cases it is population parameters, in others it is the sample statistics.
5. A statistical significance test that is based on a small sample may not produce a result that is statistically significant even if the true value of the coefficient is different from the value in the null hypothesis. Such a situation is:
   1. Power of the test
   2. Type I Error
   3. Type II Error
   4. Significance level of the test
6. Smaller p-values indicate more evidence supporting:
   1. The alternative hypothesis
   2. The null hypothesis
   3. The need for more testing
   4. The quality of the data
7. A null hypothesis of H₀: \beta = 0 can be rejected at the 95% confidence interval if and only if:
   1. The 95% confidence interval contains zero
   2. The 95% confidence interval does not contain zero
   3. The null hypothesis is in the middle of the 95% confidence interval
   4. The sample size is sufficiently large (n>=30)
8. Which of the following will tend to reduce the size of a confidence interval?
   1. Decrease the significance level (alpha).
   2. Increase the sample size
   3. Decrease the standard deviation of the population
   4. You can’t do anything to reduce the interval
9. If we decrease the significance level (alpha) all else being equal, the power of the test will:
   1. Decrease
   2. Increase
   3. Won’t change
   4. It depends – need more information
10. Explain what the distribution of ₁ is under the null hypothesis H₀: \beta = 0 and why.
11. Explain the t distribution and explain what its tails are like and why?
12. Describe the relationship between sample size and statistical significance.
13. Describe what a power curve is, and provide a rough sketch of a power curve, and accurately label the x-axis and the y-axis.
14. Explain the difference between statistical significance and substantive significance.
15. Show the full equation to calculate the t-statistic.