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Zorluk: KolayHypothesis Testing and Statistical Power

An epidemiologist is evaluating a community intervention designed to increase physical activity among adults with type 2 diabetes. Before data collection begins, the investigator sets the maximum acceptable probability of rejecting a true null hypothesis at 0.050.05. Additionally, the probability of failing to reject a false null hypothesis is set at 0.200.20. Based on these parameters, what is the statistical power of this planned intervention study?

  1. A
    5%5\%
  2. B
    20%20\%
  3. C
    75%75\%
  4. 80%80\%Cevap
  5. E
    95%95\%

Cevap

The statistical power of the study is 80%80\%.
Statistical power is defined as 1−β1 - \beta, where β\beta is the probability of committing a Type II error (failing to reject a false null hypothesis). In this scenario, β\beta is given as 0.200.20. Therefore, the statistical power is 1−0.20=0.801 - 0.20 = 0.80, or 80%80\%. This represents the study's ability to successfully detect a true effect of the community intervention if one actually exists.

Adım Adım Çözüm

1
Identify the probability of committing a Type II error (β\beta) from the clinical vignette.
β=0.20\beta = 0.20
The problem explicitly states that the probability of failing to reject a false null hypothesis is 0.200.20.
2
Apply the mathematical formula for statistical power.
Power=1−β=1−0.20=0.80\text{Power} = 1 - \beta = 1 - 0.20 = 0.80
Statistical power is defined as the probability of correctly rejecting the null hypothesis when it is truly false.

Anahtar Kavram

Statistical power is the probability of correctly rejecting a false null hypothesis, mathematically defined as 1−β1 - \beta, where β\beta is the Type II error rate.
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Hypothesis Testing and Statistical Power

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