Please help me, I don't know the answer WILL MARK BRANLIEST IF CORRECT :)
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Answer:
Yes, there is a difference between the population mean for the math scores and the population mean for the writing scores.
Test Statistics = follows
.
Step-by-step explanation:
We are provided with the sample data showing the math and writing scores for a sample of twelve students who took the SAT ;
Let A = Math Scores ,B = Writing Scores and D = difference between both
So, = Population mean for the math scores
= Population mean for the writing scores
Let = Difference between the population mean for the math scores and the population mean for the writing scores.
<em> Null Hypothesis, </em><em> : </em>
<em> or </em>
<em> = 0 </em>
<em> Alternate Hypothesis, </em><em> : </em>
<em> or </em>
<em> 0</em>
Hence, Test Statistics used here will be;
follows
where, Dbar = Bbar - Abar
=
n = 12
Student Math scores (A) Writing scores (B) D = B - A
1 540 474 -66
2 432 380 -52
3 528 463 -65
4 574 612 38
5 448 420 -28
6 502 526 24
7 480 430 -50
8 499 459 -40
9 610 615 5
10 572 541 -31
11 390 335 -55
12 593 613 20
Now Dbar = Bbar - Abar = 489 - 514 = -25
Bbar = =
= 489
Abar = =
= 514
∑ = 22600 and
=
=
= 37.05
So, Test statistics = follows
= follows
= -2.34
<em>Now at 5% level of significance our t table is giving critical values of -2.201 and 2.201 for two tail test. Since our test statistics doesn't fall between these two values as it is less than -2.201 so we have sufficient evidence to reject null hypothesis as our test statistics fall in the rejection region .</em>
Therefore, we conclude that there is a difference between the population mean for the math scores and the population mean for the writing scores.
If angle 1 and angle 2 are <u>complementary, </u>then they add up to 90 degrees. We are given that angle 2 equals 52 degrees.
So we subtract and get our answer:
38
That's NOT the final answer.
The next step is:
Angle 1 and angle 3 are vertical angles.
Vertical angles are congruent.
So if angle 1 is 38, then angle 3 is also 38.
Now, supplementary angles add up to 180 degrees.
So that's the answer:
180-38=142
142 is the supplement of angle 3.
Hope it helps! :)
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