1. In a hypothesis testing problem: Select one: a. the null hypothesis will not
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Question
1. In a hypothesis testing problem:
Select one:
a. the null hypothesis will not be rejected unless the data are not unusual (given that the hypothesis is true).
b. the null hypothesis will not be rejected unless the p-value indicates the data are very unusual (given that the hypothesis is true).
c. the null hypothesis will not be rejected only if the probability of observing the data provide convincing evidence that it is true.
d. the null hypothesis is also called the research hypothesis; the alternative hypothesis often represents the status quo.
2. If the null hypothesis is true, increasing only the sample size will increase the probability of rejecting the null hypothesis.
Select one:
a. True
b. False
3.
The risk of a Type II error is directly controlled in a hypothesis test by establishing a specific significance level.
Select one:
a. True
b. False
4. If the value of any test statistic does not fall in the rejection region, the decision is:
Select one:
a. Reject the null hypothesis.
b. Reject the alternative hypothesis.
c. Fail to reject the null hypothesis.
d. Fail to reject the alternative hypothesis.
5. The risk of a Type II error is directly controlled in a hypothesis test by establishing a specific significance level.
Select one:
a. True
b. False
Explanation / Answer
1. In a hypothesis testing problem:
b. the null hypothesis will not be rejected unless the p-value indicates the data are very unusual (given that the hypothesis is true).
This is because p-value gives the evidence that whether the test is statistically significant or not on the basis of which we accept or reject the null hypothesis.
2. If the null hypothesis is true, increasing only the sample size will increase the probability of rejecting the null hypothesis.
a. True
This is because, increase in the sample size reduce p-value and smaller the value of p the more is the probability of rejecting the null hypothesis.
3. The risk of a Type II error is directly controlled in a hypothesis test by establishing a specific significance level.
b. False
We can only indirectly control the risk of a Type II error by establishing a specific significance level, that is, type I error as decrease in one type of error results in the increase of other type of error. To control the risk of a Type II error directly we need to increase the sample size.
4. If the value of any test statistic does not fall in the rejection region, the decision is:
Select one:
c. Fail to reject the null hypothesis.
Since the value of test statistic does not fall in the rejection region we have no evidence to reject the null hypothesis.
5. The risk of a Type II error is directly controlled in a hypothesis test by establishing a specific significance level.
b. False
We can only indirectly control the risk of a Type II error by establishing a specific significance level, that is, type I error as decrease in one type of error results in the increase of other type of error. To control the risk of a Type II error directly we need to increase the sample size.
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