Two samples from the same population both have M = 84 and s² = 20,but one sample has n = 10 and the other has n = 20 scores.Both samples are used to evaluate a hypothesis stating that ? = 80 and to compute Cohen's d.How will the outcomes for the two samples compare? A)The larger sample is more likely to reject the hypothesis and will produce a larger value for Cohen's d. B)The larger sample is more likely to reject the hypothesis, but the two samples will have the same value for Cohen's d. C)The larger sample is less likely to reject the hypothesis and will produce a larger value for Cohen's d. D)The larger sample is less likely to reject the hypothesis, but the two samples will have the same value for Cohen's d.

Question

Quizplus · Accepted Answer

Cohen's d is calculated using the formula $d = \frac{M - \mu}{s}$, where $M$ is the sample mean, $\mu$ is the population mean, and $s$ is the standard deviation. Since both samples have the same mean (M = 84), the same variance (and thus the same standard deviation), and are being compared to the same population mean ($\mu = 80$), the value of Cohen's d will be the same for both samples. However, the larger sample (n = 20) is more likely to reject the hypothesis due to its greater statistical power, which comes from its larger sample size.

Two Samples from the Same Population Both Have M =