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?

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)  

2 x t divided by n

step-by-step explanation:

answer: a

step-by-step explanation: