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Bill conducts a study during which he compares two, independent groups and he gets a significance value of .16 (i.e., p=.16). He looks at the means of the groups and sees the Group 1 Mean is 70 and the Group 2 mean is 77. He concludes they are different. (a) Why is Bill wrong? (b) What exactly does his p-value mean, in this instance?

User Lreeder
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Answer:

P-value is a parameter to compare with the significance level in order to make decisions about rejecting or not the hypothesis

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)

User Eladcon
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