Statistical Test

Under conditions, when the sample size is small, say less than 30 and the population SD is not known. We can use the T-Test for Mean technique.

It is assume that the population is known to be normally distributed.

The formula for T-Test is

t = X - x / (S / SQRT(n))

Example:
Average Pulse of men is 70 beats per minutes (bpm).

A sample of 10 adults were given a new drugs, and their mean is measured to at 75 bpm and SD of 8 bpm. With a level of significant of α=0.01.

Is the change in pulse rate due to random chance?

State the null hypothesis:
"There is no significant difference in pulse between these patients and the population as a whole."
H0 = 70

State the alternative hypothesis:
"There is a significant difference in pulse between these patients and the population as a whole."
H1 <> 70

Degree of freedom (d.f.) is equal to N-1,
Since N=10, therefore d.f. = 9.

The null hypothesis is given in the form corresponding to a
two-tailed test (H0 : μ = k , H1 : μ