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 α = 0.01?

Weight	Fat
67 68 94 101 67 81 74 78 60 89 90	29 28 25 24 30 26 30 26 31 24 30

a.) Compute the statistic selected:

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 =

Make an interpretation based on the results.

More weight of individuals on the diet significantly predicts more 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
	81	26	6561	676	2106
	74	30	5476	900	2220
	78	26	6084	676	2028
	60	31	3600	961	1860
	89	24	7921	576	2136
	90	30	8100	900	2700
Total	869	303	70381	8415	23681

The statistics is: r = -0.742

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