Math  /  Data & Statistics

QuestionWhich of the following is/are True? The level of significance of a test depends on the value of the sample statistic. The level of significance depends on the alternative hypothesis. The level of significance is generally set in advance before samples are drawn The level of significance is the probability of rejecting a null hypothesis when it is in fact true.

Studdy Solution

STEP 1

1. The level of significance is a predetermined threshold used in hypothesis testing.
2. The level of significance is denoted by α\alpha and is commonly set at values like 0.05, 0.01, etc.
3. The level of significance is related to Type I error in hypothesis testing.

STEP 2

1. Evaluate the statement about the dependence on the sample statistic.
2. Evaluate the statement about the dependence on the alternative hypothesis.
3. Evaluate the statement about setting the level of significance in advance.
4. Evaluate the statement about the probability of rejecting a true null hypothesis.

STEP 3

Evaluate the statement: "The level of significance of a test depends on the value of the sample statistic."
The level of significance is a threshold set before the test and does not depend on the sample statistic. It is independent of the data collected.
Conclusion: False

STEP 4

Evaluate the statement: "The level of significance depends on the alternative hypothesis."
The level of significance is chosen by the researcher and is not directly dependent on the alternative hypothesis. However, the choice of α\alpha might be influenced by the context of the hypothesis, but it is not a direct dependency.
Conclusion: False

STEP 5

Evaluate the statement: "The level of significance is generally set in advance before samples are drawn."
The level of significance is indeed set before conducting the test to avoid bias and ensure the integrity of the test.
Conclusion: True

STEP 6

Evaluate the statement: "The level of significance is the probability of rejecting a null hypothesis when it is in fact true."
This statement is the definition of the level of significance, which is the probability of committing a Type I error.
Conclusion: True
The True statements are:
- The level of significance is generally set in advance before samples are drawn. - The level of significance is the probability of rejecting a null hypothesis when it is in fact true.

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