The effect of phosphate supplementation on bone formation wa

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

Solution

sample size,n = 6
sample mean,xbar = -2.638
standard deviation,s = 2.215
.
H0: Ud = 0
H1: Ud < 0
where \'Ud\' is true mean difference (control - phosphate)

a.
test statistic, t = (xbar-u)/(s/sqrt(n))
t = (-2.638-0) / (2.215/sqrt(6)) = -2.917
absolute value of the test statistic is 2.917

b.
degree of freedom = n-1 = 5
Since it is a 1-tailed test hence
P_value = 0.017

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