Question:

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.

Table 1: correlation among minutes of exercise, BMI and depression

Exercise in past week (minutes) BMI

BMI -0.15

Depression score -0.30 (P<0.05) 0.20

1.a research and null hypotheses regarding the relationship between exercise and depression.

2.Based on the test statistics in table 1, what is your conclusion regarding your research hypothesis? (Hint: discuss both the magnitude and direction of 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?