Sampling Distribution, Difference between Independent Means (4 of 5)
A look at a graph of the sampling distribution of Md
makes the problem
more concrete. The mean of the sampling distribution is 10 and the standard deviation
is 2.35. The graph shows the distribution. Back to the question:
What is the probability that the drug group will score 15 or more points higher?
The blue region of the graph
is 15 or higher and is a small portion of the area. The probability can be determined
by computing the number of standard deviations above the mean 15 is. Since the
mean is 10 and the standard deviation is 2.35, 15 is (15-10)/2.35 = 2.13
standard deviations above the mean. From a z table
can be determined that 0.983 of the area is below 2.13; therefore, 0.017 of the
area is above. It follows that the probability of a difference between the drug
and no-drug means of 15 or larger is .017.
As shown below, the z table
calculator allows you to compute this value
directly without using z scores.