Recall that the power of a test is the probability that we reject H_0 when H_0 is false. Which of the following are true? Select one or more answers.Group of answer choicesIf sample size increases then power increases.If H_0 is very likely to be true then the power is higher when compared to when H_0 is very likely to be false.If α increases then power increases.If the effect size increases then power increases.
Question
Recall that the power of a test is the probability that we reject H_0 when H_0 is false. Which of the following are true? Select one or more answers.Group of answer choicesIf sample size increases then power increases.If H_0 is very likely to be true then the power is higher when compared to when H_0 is very likely to be false.If α increases then power increases.If the effect size increases then power increases.
Solution 1
The correct answers are:
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If sample size increases then power increases: This is true. The power of a test increases with the sample size. The larger the sample size, the more likely we are to reject a false null hypothesis.
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If H_0 is very likely to be true then the power is higher when compared to when H_0 is very likely to be false: This is false. The power of a test is the probability of rejecting a false null hypothesis. If H_0 is true, then there is no power because there is no false null hypothesis to reject.
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If α increases then power increases: This is true. The power of a test increases as the significance level (α) increases. The higher the significance level, the more likely we are to reject a false null hypothesis.
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If the effect size increases then power increases: This is true. The power of a test increases with the effect size. The larger the effect size, the more likely we are to reject a false null hypothesis.
Solution 2
The correct answers are:
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If sample size increases then power increases: This is true. The power of a test increases with the sample size. The larger the sample size, the more likely we are to reject a false null hypothesis.
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If H_0 is very likely to be true then the power is higher when compared to when H_0 is very likely to be false: This is false. The power of a test is the probability of rejecting the null hypothesis when it is false. So, if H_0 is true, then the power of the test is not applicable.
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If α increases then power increases: This is true. The power of a test increases as the significance level (α) increases. The higher the significance level, the more likely we are to reject a false null hypothesis.
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If the effect size increases then power increases: This is true. The power of a test increases with the effect size. The larger the effect size, the more likely we are to reject a false null hypothesis.
Similar Questions
What happens to the power of a test as the sample size increases?a.The power decreasesb.The power increasesc.The power remains the samed.The power becomes undefinedClear my choice
Identify the three factors that determine the power of a statistical test.Select one or more:a.statistical treatmentb.null hypothesis testingc.level of statistical significanced.sample sizee.size of the treatment effectf.pobability
Which of the following is an accurate definition for the power of a statistical test?Group of answer choicesThe probability of rejecting a false null hypothesisThe probability of supporting a false null hypothesisThe probability of rejecting a true null hypothesisThe probability of supporting true null hypothesis
The power of a test is the probability of making:Group of answer choicesan incorrect decision when the null hypothesis is false.an incorrect decision when the null hypothesis is true.a correct decision when the null hypothesis is false.a correct decision when the null hypothesis is true.
By increasing the sample size, what change will be observed in statistical power?1 pointThe power will decrease.A change in power cannot be predicted from sample size.The power will not change.The power will increase.
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