To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ=20, and the treatment is administered to the individuals in the sample. After the treatment, the sample mean is found to be M=21.3 with a variance of s²=9. a. Assuming that the sample consists of n=16 individuals , use a two-tailed hypothesis test with α=.05 to determine whether the treatment effect is significant and compute both Cohen's d and r² to measure effect size. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05? b. Assuming that the sample consists of n=36 individuals, repeat the test and compute both measures of effect size. c. Comparing your answers for parts a and b, how does the size of the sample influence the outcome of a hypothesis test and measures of effect size?
To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ=20, and the treatment is administered to the individuals in the sample. After the treatment, the sample mean is found to be M=21.3 with a variance of s²=9.
a. Assuming that the sample consists of n=16 individuals , use a two-tailed hypothesis test with α=.05 to determine whether the treatment effect is significant and compute both Cohen's d and r² to measure effect size. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05?
b. Assuming that the sample consists of n=36 individuals, repeat the test and compute both measures of effect size.
c. Comparing your answers for parts a and b, how does the size of the sample influence the outcome of a hypothesis test and measures of effect size?
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