In conducting a hypothesis test for the difference in two population means where the standard
deviations are known and the null hypothesis is:
o H : uA - uB ≥ 0
What is the p-value assuming that the test statistic has been found to be z = 2.52?
A) 0.0059
B) 0.9882
C) 0.0118
D) 0.4941
How about A)? (Check a z-table. P-value is the actual level of the test statistic.)
To find the p-value in this hypothesis test, we need to determine the probability of observing a test statistic as extreme as the one we have calculated, assuming the null hypothesis is true.
The test statistic in this case is a z-value of 2.52. To find the p-value, we will use the standard normal distribution.
First, we need to find the area under the standard normal curve to the right of the z-value. We can use a standard normal table or a calculator to find this area.
Using a standard normal table, we look up the z-value of 2.52 and find the corresponding area to the right of this value. Let's call this area A.
Since the null hypothesis is "uA - uB ≥ 0," we are interested in the area to the right of the z-value (2.52) because we want to find the probability of obtaining a test statistic as extreme or more extreme than the observed one (2.52).
The p-value is the probability of observing a value as extreme or more extreme than the test statistic assuming the null hypothesis is true. In this case, it is the area to the right of the z-value (A).
To find the p-value, we need to subtract A from 1 (the total area under the standard normal curve).
Therefore, the p-value is 1 - A.
Now, if we consult a standard normal table or use a calculator, we find that the area to the right of a z-value of 2.52 is approximately 0.0059.
So, the p-value is 1 - 0.0059 = 0.9941.
Therefore, the correct answer is not listed among the options provided.