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Homework 06 - Answers and Points

Homework 06 - Answers and Points - HomeworkAssignment6...

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Psychology 60 Spring 2010 Homework Assignment 6 For homework problems requiring calculation, you must show all of your work, including intermediate steps, in order to receive credit. 1) Find the t critical values for a two‐tailed hypothesis test with α = 0.05 for the follow values of df: a. (1 point) df = 2 t critical = ± 4.303 b. (1 point) df = 8 t critical = ± 2.306 c. (1 point) df = 20 t critical = ± 2.086 d. (1 point) df = 40 t critical = ± 2.021 2) The following scores were obtained from a population with unknown parameters. Scores: 6, 12, 0, 3, 4 a. (1 point) Compute the sample mean X = Σ X i n , X = 25 5 , X = 5 b. (2 points) Compute the estimate of the population variance s 2 = SS n 1 , SS = Σ ( X i X ) 2 SS = (6 5) 2 + (12 5) 2 + (0 5) 2 + (3 5) 2 + (4 5) 2 = 80 s 2 = 80 4 , s 2 = 20 c. (2 points) Compute the estimate of the standard error, s X s X = s 2 n , s X = 20 5 , s X = 4 , s X = 2 3) To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be X = 33 a. (6 points total ) If the sample has a variance of s 2 =81, are the data sufficient to conclude that the treatment has a statistically significant effect using a two‐tailed test with α = 0.05 ? (2 points) s X = s 2 n , s X = 81 9 , s X = 9 , s X = 3
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(2 points) t X = X μ s X , t X = 33 40 3 , t X = 7 3 , t X = 2.33 (1 point) df = 8, α = 0.05 , t critical = ± 2.306 (1 point) |t observed | > |t critical |, |-2.33| > |2.306|, Reject Null Hypothesis b. (6 points total ) If the sample has a variance of s 2 =225, are the data sufficient to conclude that the treatment has a statistically significant effect using a two‐tailed test with α = 0.05 ?
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