A NP researcher randomly sampled 100 women aged 50-65 years and measured their minutes of exercise in the past week, BMI, and depression. Depression was measured using a Likert type scale consisting of 20 items. The summation score ranged from 20 to 100 and the higher the score, the higher the level of depression.The Pearson correlation coefficients (r's) are summarized in the following table. For the analyses, statistical significant level was set at =0.05.

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Table 1

Correlation among minutes of exercise, BMI and depression*p < 0.05

Exercise in past week (min) BMI

BMI -0.15

Depression Score -0.30* 0.20

1.Write aresearch question for the relationship betweenexercise and depression. Express thenullandalternativehypotheses symbolically.

2.Based on the estimates provided in table 1, what is your conclusion regarding your research hypothesis? (Discussboththemagnitudeanddirectionof the relationship).

3.What proportion of variance is shared by minutes of exercise and depression among women 50-65 years of age?

4.For the relationship between minutes of exercise and BMI,

a.what was the estimated power of the statistical test? (Using the power table on page 202, table 9.1, Polit 2010).

b.What was the risk that a type II error was committed?

5.If -0.20 is a good estimation of population correlation, what sample size would be needed to achieve power of 0.80 at a significance =0.05?