1. A researcher has just finished a statistical analysis and claims that he found evidence that...
1.
A researcher has just finished a statistical analysis and claims that he found evidence that x affects y positively. Using a 1-tailed test, he found that the estimated coefficient for x is significantly positive at the 5% level, but is not significant at the 4% level. Assume that the classical linear regression assumptions hold. If the researcher used a 2-tailed test instead, what would he have found?
| a. |
The estimated coefficient for x is significantly positive at the 2.5% level. |
|
| b. |
The estimated coefficient for x is significantly positive at the 10% level. |
|
| c. |
The estimated coefficient for x is significantly positive at the 5% level. |
|
| d. |
The estimated coefficient for x is significantly positive at the 4% level. |
2.
Which of the following statements is true?
| a. |
Taking a log of a nonnormal distribution may yield a distribution that is closer to normal. |
|
| b. |
The mean of a nonnormal distribution is 0 and the variance is σ2. |
|
| c. |
OLS estimators have the highest variance among unbiased estimators. |
|
| d. |
The CLT assumes that the dependent variable is unaffected by unobserved factors. |
3.
The normality assumption implies that:
| a. |
the population error u is dependent on the explanatory variables and is normally distributed with mean equal to one and variance σ2. |
|
| b. |
the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance σ. |
|
| c. |
the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance σ. |
|
| d. |
the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance σ2. |
Homework Answers
1)b) This is because at one tailed it is significantly positive at 5% level hence for a two tailed it definitely would be at 10% level.
2)a) It coverts a non normal distribution to normal by taking log.
3)d) The population error u is always independent of the explanatory variables and is normally distributed with mean zero and variance sigma square.
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