If the mean for group 1 in a clinical trial for the time for a drug X to act is 10 minutes and 8 minutes for group 2 and if the standard deviation for group 1 is 1.0 and group 2 is 2.0. If there are 4 persons in both groups, what is the t value and which hypothesis would you accept if t critical is 3.14 ( 2 sided).
The t value is calculated by subtracting the means of the two groups and dividing by the square root of the sum of the variances of the two groups.
t = (10 - 8) / sqrt(1^2 + 2^2) = 2 / sqrt(5) = 0.894
Since the t value is less than the t critical value of 3.14, we would accept the null hypothesis that there is no significant difference between the two groups.