Multiple Choice – Choose the best option and then provide an explanation for why
ID: 3156141 • Letter: M
Question
Multiple Choice – Choose the best option and then provide an explanation for why that is the best choice
a) If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000. Justify your answer.
A) either a one-tail or two-tail test could be used with equivalent results.
B) a one-tail test should be utilized.
C) a two-tail test should be utilized.
D) None of the above.
b) If the p-value is less than in a two-tail test, Justify your answer.
A) the null hypothesis should not be rejected.
B) the null hypothesis should be rejected.
C) a one-tail test should be used.
D) no conclusion should be reached.
c) If a test of hypothesis has a Type I error probability () of 0.01, we mean. Justify your answer.
A) if the null hypothesis is true, we don't reject it 1% of the time.
B) if the null hypothesis is true, we reject it 1% of the time.
C) if the null hypothesis is false, we don't reject it 1% of the time.
D) if the null hypothesis is false, we reject it 1% of the time.
d) If the Type I error () for a given test is to be decreased, then for a fixed sample size n. Justify your answer.
A) the Type II error () will also decrease.
B) the Type II error () will increase.
C) the power of the test will increase.
D) a one-tail test must be utilized.
e) For a given sample size n, if the level of significance () is decreased, the power of the test. Justify your answer.
A) will increase.
B) will decrease.
C) will remain the same.
D) cannot be determined.
Explanation / Answer
a)
C) a two-tail test should be utilized. [ANSWER]
He doesn't care if the true mean is greater or less than $50000. He just wants to know whether or not it is equal to $50000. Hence, two tailed.
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b)
B) the null hypothesis should be rejected. [ANSWER]
We always reject Ho when P < alpha.
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c)
OPTION B: B) if the null hypothesis is true, we reject it 1% of the time. [ANSWER]
This is by definition of alpha.
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