Question: Multiple Choice – Choose the best option and then provide an explanation for why that is the best choice. (4 pts each: correct answer – 2 pts, correct explanation – 2 pts)

1. If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000
   1. either a one-tail or two-tail test could be used with equivalent results.
   2. a one-tail test should be utilized.
   3. a two-tail test should be utilized.
   4. None of the above.
2. If the p -value is less than α in a two-tail test,
   1. the null hypothesis should not be rejected.
   2. the null hypothesis should be rejected.
   3. a one-tail test should be used.
   4. no conclusion should be reached.
3. If a test of hypothesis has a Type I error probability ( α ) of 0.01, we mean
   1. if the null hypothesis is true, we don't reject it 1% of the time.
   2. if the null hypothesis is true, we reject it 1% of the time.
   3. if the null hypothesis is false, we don't reject it 1% of the time.
   4. if the null hypothesis is false, we reject it 1% of the time.
4. If the Type I error ( α ) for a given test is to be decreased, then for a fixed sample size n
   1. the Type II error ( β ) will also decrease.
   2. the Type II error ( β ) will increase.
   3. the power of the test will increase.
   4. a one-tail test must be utilized.
      The answer is B) the Type II error ( β ) will increase.
5. For a given sample size n , if the level of significance ( α ) is decreased, the power of the test
   1. will increase.
   2. will decrease.
   3. will remain the same.
   4. cannot be determined.

The answer is B) will decrease .

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