Final answer:
To find the number of participants needed for a medium correlation of 0.30 in power analysis, use the sample size formula for a correlation test.
Step-by-step explanation:
To determine the number of participants needed for a medium correlation of 0.30 in power analysis, we need to use a power analysis formula. In this case, we can use the sample size formula for a correlation test:
n = (Zα/2 + Zβ)^2 * (1 - r^2) / r^2
Where:
n = sample size
Zα/2 = critical value for a two-tailed test (e.g., for a 95% confidence level, Zα/2 = 1.96)
Zβ = critical value for the desired power (e.g., for 80% power, Zβ ≈ 0.84)
r = correlation coefficient (0.30 in this case)
Plugging in the values, we get:
n = (1.96 + 0.84)^2 * (1 - 0.30^2) / 0.30^2
Simplifying the equation, we find that the number of participants needed is approximately 85 (option A).