Answer:
P-value is a parameter to compare with the significance level in order to make decisions about rejecting or not the hypothesis
Step-by-step explanation:
When you are developing a hypothesis test, in order to compare two means ( μ₁ and μ₂ ) you have two hypothesis
Null Hypothesis H₀ μ₁ = μ₂
And depending on the problem statement, the alternative hypothesis could be
Alternative Hypothesis Hₐ (1) μ₁ > μ₂
(2) μ₁ < μ₂
(3) μ₁ ≠ μ₂
Now if the result of the test determines that H₀ is rejected you accept in case
(1) μ₁ > μ₂
(2) μ₁ > μ₂
(3) μ₁ ≠ μ₂
In any case, you need a confidence Interval, and as consequence you established a significance level to do your test. These two concept defines the acceptance and the rejection region. Just for instance
CI = 90% means that the acceptance region is 90 %, and at the same time, the rejection area is 10 %. That 10 % will be used as follows,
Case 1 you are developing a one tail-test to the left ( side of the curve )
Case 2 you are developing a one tail-test to the right
Case 3 you are developing a two-tail test ( in that case you need to split α into two equal areas one for each tail.
Now P-value is a tool for decision is an area that you can compare with α to accept or reject H₀.
In our particular case suppose we are testing
H₀ μ₁ = μ₂
Hₐ μ₁ < μ₂
Let´s say CI = 95 then α = 5 % α = 0,05
And we get P-value = 0,16
Then area 0,16 > 0,05 Then we are in the acceptance region
(that condition really implies that z(s) < z(c)
