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Aleksandr-060686 [28]

3 years ago

11

How to solve number 13

1 answer:

noname [10]3 years ago

8 0

$\bf \cfrac{3x-1}{x+2}-\cfrac{x-2}{x-1}\impliedby \stackrel{our~LCD~is}{(x+2)(x-1)} \\\\\\ \cfrac{(3x-1)(x-1)-\stackrel{\textit{difference of squares}}{(x-2)(x+2)}}{(x+2)(x-1)} \\\\\\ \cfrac{(3x^2-4x+1)-(x^2-2^2)}{(x+2)(x-1)}\implies \cfrac{(3x^2-4x+1)-(x^2-4)}{(x+2)(x-1)} \\\\\\ \cfrac{3x^2-4x+1-x^2+4}{x^2+x-2}\implies \cfrac{2x^2-4x+5}{x^2+x-2}$

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Answer:

Brand 1 Brand 2 Difference

37734 35202 2532

45299 41635 3664

36240 35500 740

32100 31950 150

37210 38015 −805

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33500 33215 285

Sum of difference = 2532+ 3664+740+150 −805+ 560 +390 +285 = 7516

Mean = $d=\frac{7516}{8}$

Mean = $d=939.5$

a) d= 939.5

$\text{Sample Standard deviation, s} = \sqrt{\dfrac{(x-\bar{x})^2}{n-1}}$

$=\sqrt{\dfrac{(2532-939.5)^2+(3664-939.5)^2+(740-939.5)^2 ...+(285-939.5)^2}{8-1}}$

=1441.21

b)SD= 1441.21

c)Calculate a 99% two-sided confidence interval on the difference in mean life.

confidence level =99%

significance level =α= 0.01

Degree of freedom = n-1 = 8-1 =7

So, $t_{\frac{\alpha}{2}}=3.499$

Formula for confidence interval $= \left( \bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}} \right)$

Substitute the values

confidence interval $= 939.5 \pm 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$

confidence interval $= 939.5 - 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$ to $= 939.5 + 3.499 \times \frac{1441.21}{\sqrt{8}} \right)$

Confidence interval $−843.396\$ to $2722.396$

8 0

3 years ago