A researcher is investigating the effectiveness of a new treatment for improving short-term memory. A sample of n = 8 participants is obtained. Each individual completes a short-term memory test and then begins a 4-week program of the new treatment. At the end of the program, the short-term memory is tested again and the researcher records the amount of difference between the two ratings. For this sample, memory scores increased by an average of M = 3.5 points with SS = 56. Can you conclude that the new treatment significantly improves (increases) short-term memory performance? Test with α = .05, one-tailed. a. state the null and alternative hypotheses b. Locate the boundary of the critical region c.  Calculate the test statistic. t = ? d. what is the correct decision? e. Compute r2 to measure the size of the treatment effect. (Round to three decimal places)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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A researcher is investigating the effectiveness of a new treatment for improving short-term memory. A sample of n = 8 participants is obtained. Each individual completes a short-term memory test and then begins a 4-week program of the new treatment. At the end of the program, the short-term memory is tested again and the researcher records the amount of difference between the two ratings. For this sample, memory scores increased by an average of M = 3.5 points with SS = 56. Can you conclude that the new treatment significantly improves (increases) short-term memory performance? Test with α = .05, one-tailed.

a. state the null and alternative hypotheses

b. Locate the boundary of the critical region

c.  Calculate the test statistic. t = ?

d. what is the correct decision?

e. Compute r2 to measure the size of the treatment effect. (Round to three decimal places)

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