Kathy Guerra

2022-10-09

Showing power curves for a one-sided t-test. Use the figure to give the approximate power in each of the following situations, and write a sentence explaining what probability is represented by the power. n = 20, true effect size = 0.4. n = 50, true effect size = 0.4. n = 100, true effect size = 0.4. n = 20, true effect size = 0.7.

Kaleb Harrell

Beginner2022-10-10Added 14 answers

a) Project the value d=0.4 from the horizontal axis onto the purple curve labeled "n=20". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 0.5. This value means that the probability of rejecting the null hypothesis is about 0.5, given that the true effect size is 0.4.

b) Project the value d=0.4 from the horizontal axis onto the red curve labeled "n=50". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 0.85. This value means that the probability of rejecting the null hypothesis is about 0.85, given that the true effect size is 0.4.

c) Project the value d=0.4 from the horizontal axis onto the green curve labeled "n=100". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 1. This value means that the probability of rejecting the null hypothesis is about 1, given that the true effect size is 0.4.

d) Project the value d=0.7 from the horizontal axis onto the purple curve labeled "n=20". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 0.9. This value means that the probability of rejecting the null hypothesis is about 0.9, given that the true effect size is 0.7.

Answer: a) 0.5; b) 0.85; c) 1; d) 0.9.

b) Project the value d=0.4 from the horizontal axis onto the red curve labeled "n=50". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 0.85. This value means that the probability of rejecting the null hypothesis is about 0.85, given that the true effect size is 0.4.

c) Project the value d=0.4 from the horizontal axis onto the green curve labeled "n=100". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 1. This value means that the probability of rejecting the null hypothesis is about 1, given that the true effect size is 0.4.

d) Project the value d=0.7 from the horizontal axis onto the purple curve labeled "n=20". Then, project that point onto the vertical axis and read the power from the scale on the axis. Approximately, the power would be about 0.9. This value means that the probability of rejecting the null hypothesis is about 0.9, given that the true effect size is 0.7.

Answer: a) 0.5; b) 0.85; c) 1; d) 0.9.

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