Question

A clinic developed a diet to impact body mass (fat and muscle). A nutritionist in the clinic hypothesizes that heavier individuals on the diet will predict more body fat. Below are the data for a sample of clients from the clinic. Weight is measured in kilograms (kg) and percentage body fat is estimated through skinfold measurement. What can the nutritionist conclude with an α of 0.05?

Weight	Fat
67 68 94 101 67 83 74 78 60 90 90	29 28 25 24 30 26 30 26 31 24 30

a) What is the appropriate statistic?
---Select--- na Correlation Slope Chi-Square
Compute the statistic selected a):

b) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
Critical value =  ; Test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =  ;   ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

More weight of individuals on the diet significantly predicts more body fat.More weight of individuals on the diet significantly predicts less body fat.    The weight of individuals on the diet does not significantly predict body fat.

Answer 1

Here we need to find the relationship between weight and fat so correlation coefficient should be used.

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	67	29	4489	841	1943
	68	28	4624	784	1904
	94	25	8836	625	2350
	101	24	10201	576	2424
	67	30	4489	900	2010
	83	26	6889	676	2158
	74	30	5476	900	2220
	78	26	6084	676	2028
	60	31	3600	961	1860
	90	24	8100	576	2160
	90	30	8100	900	2700
Total	872	303	70888	8415	23757

The statistics is: r = -0.755

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c)

Here effect size will be r square. So,

It is medium effect size.

(d)

Conclusion: More weight of individuals on the diet significantly predicts more body fat.