Which of the following statements best describes the level of significance?Group of answer choicesThe larger the level of significance, the smaller the rejection region.The larger the level of significance, the larger the probability of a Type II error.The smaller the level of significance, the smaller the rejection region.None of the other choices is correct.
Question
Which of the following statements best describes the level of significance?Group of answer choicesThe larger the level of significance, the smaller the rejection region.The larger the level of significance, the larger the probability of a Type II error.The smaller the level of significance, the smaller the rejection region.None of the other choices is correct.
Solution
The correct answer is: The smaller the level of significance, the smaller the rejection region.
Explanation:
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The level of significance, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true. It is essentially the risk of making a Type I error.
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The rejection region is the range of values for which we reject the null hypothesis. The size of the rejection region is directly related to the level of significance.
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A smaller level of significance means that we require stronger evidence to reject the null hypothesis, thus the rejection region is smaller.
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Conversely, a larger level of significance means that we are more willing to reject the null hypothesis, thus the rejection region is larger.
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Therefore, the statement "The smaller the level of significance, the smaller the rejection region" is correct.
Similar Questions
Which of the following statements is true regarding the significance level in hypothesis testing?a.It is the probability of a Type 1 errorb.It is the probability of a Type 2 errorc.It is the probability of correctly accepting the null hypothesisd.It is the probability of correctly rejecting the null hypothesisClear my choice
In the context of the level of significance, when does a Type II error occur?Multiple choice question.When the group means are equalWhen the group means are unequalWhen a true hypothesis is rejectedWhen a false hypothesis is accepted
The level of significance is the ___.Group of answer choicesmaximum allowable probability of Type I errormaximum allowable probability of Type II errorsame as the confidence coefficientsame as p-value
Which of the following statements regarding hypothesis test is FALSE?a. There is a trade-off between the probability of Type I and the probability of Type II errors.b.The smaller the significance level, the smaller the probability of a Type I error.c.If the null hypothesis is true, the distribution of the test statistic is standard normal.d.The higher the probability of a type I error, the higher the likelihood that we will retain a false null hypothesis.
If a hypothesis is rejected at the 0.025 level of significance, it:Group of answer choicesmust be rejected at any level.must not be rejected at the 0.01 level.must be rejected at the 0.01 level.may be rejected or not rejected at the 0.01 level.
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