Question

Il. You test your diabetes drug (to control blood glucose levels) in laboratory rats which are genetically engineered to have diabetes. You give the drug to six (6) of your diabetic rats, and give another six (6) diabetic rats a placebo (which does not contain the drug), and compare blood glucose levels in the two groups of rats. The measurements of blood glucose levels for both groups of rats, along with means and standard deviations for each group, are given below. Group 1 (drug-treated) Group 2 (placebo) Blood Glucose (mM) Blood Glucose (MM) 4.9 5.2 5.5 5.1 7.1 6.6 6.2 6.0 5.7 6.8 Mean ( Standard Deviation): 6.0 5.4 (0.4) 7.1 6.6 (0.5) 1. Calculate an appropriate calculated t-statistic (i.e., t-calculated) to compare the blood glucose level of the two groups of rats, i.e., "drug-treated" and "placebo." (2 pts.) t-calculated:

Answer 1

t-statistic is calculated by using formula

t = x1 - x2/√( sd1^2/n + sd2^2/n)

x1 and x2 are mean of group1 and group2 respectively

sd1 and sd2 are standard deviation of group 1 and group2 respectively.

sd1^2 means square of sd1 and sd2^2 means square of sd2

Putting all the given values in formula

t = 5.4 - 6.6 / √( 0.4^2 / 6 + 0.5^2 / 6)

-1.2 / √( .16/6 + 0.25/6)

= -1.2 / √(0.41/6)

= -1.2 / √0.683

= -1.2 / 0.261

= -4.597

So t-calculated = -4.597

We can further compare it by applying hypothesis.

Null hypothesis: x1= x2 ; x1 - x2 =0

It does not follow in this case.

Alternative hypothesis: x1>x2 ; x1<x2; x1 not equal to x2

So here significant is x1<x2

Hope this helps!!!! Thank you