Question

In the following research, identify 1. test type, 2. null hypothesis, 3. alternate hypothesis, 4. test statistic, 5. p-value, and 6. conclusion.

Researchers examined the effect of phosphate supplementation on bone formation in six healthy adult dogs. For each dog, bone formation was measured twice: once after 12 weeks of phosphate supplementation and once after a 12-week control period. The results in percent bone growth are shown below. Do the data provide evidence that phosphate supplementation significantly stimulates bone formation?

Dog ID	A	B	C	D	E	F	Avg. difference = 2.63, s=2.21
% growth Control	1.73	3.37	3.59	2.05	1.86	3.60
% growth Phosphate	8.16	4.58	3.98	5.24	3.04	7.03

Answer 1

  Average difference in percentage growth in bone formation between phosphate supplement and control period

Difference : % growth phosphate - % Growth control

1.Test Type : Paired t -test : Tests whether the mean of the differences between dependent or paired observations is equal to a target value; For the given case ; target value is zero)

2.Null hypothesis : ; phosphate supplementation does not stimulate bone formation

3.Alternate Hypothesis : phosphate supplementation stimulates bone formation

Right tailed test

4.

Test Statistic

Given,

Sample Average difference : = 2.63

Sample standard deviation of differences : s_d = 2.21

Sample size : n= 6

Degrees of freedom = n-1 =5

Test Statistic = 2.915

5. p-value

For right tailed test : p-value

6. Conclusion:

If = 0.05

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0166 < 0.05:Level of significance); Reject Null Hypothesis

The data does provide evidence that phosphate supplementation significantly stimulates bone formation

If = 0.01

As P-Value i.e. is greater than Level of significance i.e (P-value:0.0166 > 0.01:Level of significance); Fail to Reject Null Hypothesis

The data does not provide evidence that phosphate supplementation significantly stimulates bone formation