Respuesta :
Answer:
Brand 1 Brand 2 Difference
37734 35202 2532
45299 41635 3664
36240 35500 740
32100 31950 150
37210 38015 −805
48360 47800 560
38200 37810 390
33500 33215 285
Sum of difference = 2532+ 3664+740+150 −805+ 560 +390 +285 = 7516
Mean = [tex]d=\frac{7516}{8}[/tex]
Mean = [tex]d=939.5[/tex]
a) d= 939.5
[tex]\text{Sample Standard deviation, s} = \sqrt{\dfrac{(x-\bar{x})^2}{n-1}}[/tex]
[tex]=\sqrt{\dfrac{(2532-939.5)^2+(3664-939.5)^2+(740-939.5)^2 ...+(285-939.5)^2}{8-1}}[/tex]
=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, [tex]t_{\frac{\alpha}{2}}=3.499[/tex]
Formula for confidence interval [tex]= \left( \bar{X} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}} \right)[/tex]
Substitute the values
confidence interval [tex]= 939.5 \pm 3.499 \times \frac{1441.21}{\sqrt{8}} \right)[/tex]
confidence interval [tex]= 939.5 - 3.499 \times \frac{1441.21}{\sqrt{8}} \right)[/tex] to [tex]= 939.5 + 3.499 \times \frac{1441.21}{\sqrt{8}} \right)[/tex]
Confidence interval [tex] −843.396\[/tex] to [tex]2722.396[/tex]
