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jeka57 [31]
3 years ago
9

Algebra 2 question need help thanks.​

Mathematics
1 answer:
zysi [14]3 years ago
4 0
B is the correct answer
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The College Board SAT college entrance exam consists of three parts: math, writing and critical reading (The World Almanac 2012)
Wittaler [7]

Answer:

Yes, there is a difference between the population mean for the math scores and the population mean for the writing scores.

Test Statistics =   \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1 .

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, \mu_A = Population mean for the math scores

       \mu_B = Population mean for the writing scores

 Let \mu_D = Difference between the population mean for the math scores and the population mean for the writing scores.

            <em>  Null Hypothesis, </em>H_0<em> : </em>\mu_A = \mu_B<em>     or   </em>\mu_D<em> = 0 </em>

<em>      Alternate Hypothesis, </em>H_1<em> : </em>\mu_A \neq  \mu_B<em>      or   </em>\mu_D \neq<em> 0</em>

Hence, Test Statistics used here will be;

            \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1    where, Dbar = Bbar - Abar

                                                               s_D = \sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}}

                                                               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 = \frac{\sum B_i}{n} = \frac{474+380+463+612+420+526+430+459+615+541+335+613}{12}  = 489

 Abar =  \frac{\sum A_i}{n} = \frac{540+432+528+574+448+502+480+499+610+572+390+593}{12} = 514

 ∑D_i^{2} = 22600     and  s_D = \sqrt{\frac{\sum D_i^{2}-n*(Dbar)^{2}}{n-1}} = \sqrt{\frac{22600 - 12*(-25)^{2} }{12-1} } = 37.05

So, Test statistics =   \frac{Dbar - \mu_D}{\frac{s_D}{\sqrt{n} } } follows t_n_-  _1

                            = \frac{-25 - 0}{\frac{37.05}{\sqrt{12} } } follows t_1_1   = -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.

8 0
3 years ago
If the point A is located at ( –5, – 3) and A’ is the image of A after being rotated about the origin by 270° (counter clockwise
Ede4ka [16]

Answer:

A'(- 3, 5 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 270°

a point (x, y ) → (y, - x ), hence

A(- 5, - 3 ) → A'(- 3, 5 )

5 0
3 years ago
The Cunninghams are moving across the country. Mr. Cunningham leaves 3 hours before Mrs. Cunningham. If he averages 40mph and sh
svp [43]
Recall your d = rt, distance = rate * time

now, if say, by the time they meet, Mr Cunningham has travelled "d" miles, that means Mrs Cunningham must also had travelled "d" miles as well.

However, he left 3 hours earlier, so by the time he travelled "d" miles, and took say "t" hours, for her it took 3 hour less, because she started driving 3 hours later, so, she's been on the road 3 hours less than Mr Cunningham, so by the time they meet, Mrs Cunningham has travelled then "t - 3" hours.

\bf \begin{array}{lccclll}&#10;&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\&#10;&------&------&------\\&#10;\textit{Mr Cunningham}&d&40&t\\&#10;\textit{Mrs Cunningham}&d&80&t-3&#10;\end{array}&#10;\\\\\\&#10;\begin{cases}&#10;\boxed{d}=40t\\&#10;d=80(t-3)\\&#10;----------\\&#10;\boxed{40t}=80(t-3)&#10;\end{cases}&#10;\\\\\\&#10;\cfrac{40t}{80}=t-3\implies \cfrac{t}{2}=t-3\implies t=2t-6\implies 6=2t-t&#10;\\\\\\&#10;6=t
5 0
3 years ago
Find the value of n .<br> 6/n = 24/28<br> y = ___.
il63 [147K]

Answer:

n=7

Step-by-step explanation:

Cross multiply, isolate the variable, and divide by the coefficient to solve.

\frac{6}{n}=\frac{24}{28} \\ \\ 24n=168 \\ \\ n=7

Plug back in to check.

\frac{6}{7}=0.857142857 \\ \\ \frac{24}{28} =0.857142857

5 0
3 years ago
Divide (- 6 + i)/(1 - 2i) =
Kaylis [27]

~~~\dfrac{(-6 +i)}{(1- 2i)}\\\\\\=\dfrac{(-6+i)(1+2i)}{(1-2i)(1+2i)}\\\\\\=\dfrac{-6-12i+i+2i^2}{1-(2i)^2}\\\\\\=\dfrac{-6-11i-2}{1+4}~~~~~~~~~~~~~;[i^2=-1]\\\\\\=\dfrac{-8-11i}{5}\\\\\\=-\dfrac 85-\dfrac{11}{5}i

4 0
1 year ago
Read 2 more answers
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