Question

This prompt is for the next 8 questions. A researcher conducts a study examining the effectiveness of a group exercise program for elderly adults at an assisted living facility. One group of residents is selected to participate in the program, and a second group serves as a control group. After the program, the researcher measures each person’s strength. The data are as follows: Control Exercise n = 10 n = 15 top enclose x = 12 top enclose x = 15.5 sigma2 = 13.39 sigma2 = 13.57 What type of test statistic should you use? Z-test Single sample t-test Independent t-test Dependent (repeated measures) t-test QUESTION 15 What is the degrees of freedom? 9 14 23 25 QUESTION 16 What is the tcritical value? +/- 1.708 +/- 1.714 +/- 2.060 +/- 2.069 QUESTION 17 What is the SE? 0.95 1.16 1.50 5.75 QUESTION 18 What is the tobt value? 1.14 2.33 2.70 10.33 QUESTION 19 Is there a statistically significant effect (conclusion)? Yes, reject the null. Yes, failed to reject the null. No, failed to reject the null. No, reject the null. QUESTION 20 What is the effect size? (Cohen’s ds) 0.19 0.41 0.95 1.21 QUESTION 21 What is the coefficient of determination? (r2, see formula sheet) 0.19 0.41 0.95 1.21 QUESTION 22 For a one-tailed test with df =11, what is tcv at α = .05? 1.796 2.201 1.363 1.895

Answer 1

This prompt is for the next 8 questions. A researcher conducts a study examining the effectiveness of a group exercise program for elderly adults at an assisted living facility. One group of residents is selected to participate in the program, and a second group serves as a control group. After the program, the researcher measures each person’s strength. The data are as follows: Control Exercise n = 10 n = 15 top enclose x = 12 top enclose x = 15.5 sigma2 = 13.39 sigma2 = 13.57

What type of test statistic should you use? Independent t-test

QUESTION 15 What is the degrees of freedom? 23

QUESTION 16 What is the tcritical value? +/- 2.069

QUESTION 17 What is the SE? 1.50

QUESTION 18 What is the tobt value? 2.33

QUESTION 19 Is there a statistically significant effect (conclusion)? Yes, reject the null.

QUESTION 20 What is the effect size? (Cohen’s ds) 0.95

d= 3.5/ =SQRT((9*13.39+14*13.57)/23) = 0.9526

QUESTION 21 What is the coefficient of determination? (r2, see formula sheet) 0.19

r² = d² / (d² +4).= =0.9526^2/(0.9526^2+4)=0.1845

QUESTION 22 For a one-tailed test with df =11, what is tcv at α = .05? 1.796

Excel used for calculations.

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	10
Sample Mean	12
Sample Standard Deviation	3.659234893
Population 2 Sample
Sample Size	15
Sample Mean	15.5
Sample Standard Deviation	3.683748091
Intermediate Calculations
Population 1 Sample Degrees of Freedom	9
Population 2 Sample Degrees of Freedom	14
Total Degrees of Freedom	23
Pooled Variance	13.4996
Standard Error	1.5000
Difference in Sample Means	-3.5000
t Test Statistic	-2.3334
Two-Tail Test
Lower Critical Value	-2.0687
Upper Critical Value	2.0687
p-Value	0.0287
Reject the null hypothesis

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