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)  

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation: