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A developmental psychologist plans a study with the recommended adequate statistical power of .80.80. If the expected relationship between variables actually exists in the population, what is the mathematical probability (expressed as a percentage) that the study will fail to detect this relationship and thus fail to reject the null hypothesis? Show the calculation.

Question: A developmental psychologist plans a study with the recommended adequate statistical power of .80.80. If the expected relationship between variables actually exists in the population, what is the mathematical probability (expressed as a percentage) that the study will fail to detect this relationship and thus fail to reject the null hypothesis? Show the calculation.

Sample answer: Since the study design has an 80%80\% chance of successfully detecting a true relationship (statistical power of .80.80), the probability of failing to detect it is the complement of this success rate: 100%80%=20%100\% - 80\% = 20\%. Therefore, the probability that the study will fail to reject the null hypothesis is 20%20\%.

Key points:

  • The baseline statistical power is .80.80 (or 80%80\%).
  • The calculation is 100%80%=20%100\% - 80\% = 20\% (or 10.80=0.201 - 0.80 = 0.20).
  • The final probability of failing to reject the null hypothesis is 20%20\%.

Rubric: To earn full credit, the response must: 1. Apply the .80.80 (or 80%80\%) power value to determine the success rate of detecting a true effect. 2. Show the calculation subtracting the success rate from the total probability (100%80%100\% - 80\% or 10.801 - 0.80). 3. State the final probability of failing to reject the null hypothesis as 20%20\% (or 0.200.20).

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Updated 2026-05-26

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Research Methods in Psychology - 4th American Edition @ KPU

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