Question

The effect of phosphate supplementation on bone formation was assessed in 6 healthy adult dogs. For each dog, bone formation was measured for a 12-week period of phosphate supplementation as well as for a 12-week control period. Here are the results in percent growth per year:

Dog: 1 2 3 4 5 6
Control: 1.73 3.37 3.59 2.05 1.86 3.6
Phosphate: 8.16 4.58 3.98 5.24 3.04 7.03
A researcher is interested in investigating if phosphate supplementation results in significant increase in growth rate of dogs. Answers must be correct up to three decimal places.

(a) The absolute value of the test statistic is


(b) The p-value of the test is

Answer 1

Ho :   µd=   0
Ha :   µd <   0

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
1.73	8.16	-6.430	14.377
3.37	4.58	-1.210	2.040
3.59	3.98	-0.390	5.055
2.05	5.24	-3.190	0.304
1.86	3.04	-1.180	2.127
3.6	7.03	-3.430	0.627

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	16.2	32.03	-15.830	24.530

mean of difference ,    D̅ =ΣDi / n =   -2.638                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    2.2149                  
                          
std error , SE = Sd / √n =    2.2149   / √   6   =   0.9042      
                          
t-statistic = (D̅ - µd)/SE = (   -2.638 -   0   ) /    0.9042   =   -2.918

a)

(a) The absolute value of the test statistic is = 2.918

b) Degree of freedom, DF=   n - 1 =    5  
  
p-value =        0.017 [excel function: =t.dist(t-stat,df) ]

Since P_value < 0.05, hence reject H0
So, we conclude that phosphate supplementation results in significant increase in growth rate of dogs.