We can use the slope formula to find the slope.
2 + 5 / 4 - 0
7/4
The slope is 7/4, or 1.75
Answer:
Right answer is choice D.
Answer:
We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm
Step-by-step explanation:
Sample Information:
Results:
41.8
40.9
42.1
41.2
40.5
41.1
42.6
40.6
From the table we get:
sample mean : x = 41.35
sample standard deviation s = 0.698
Hypothesis Test:
Null Hypothesis H₀ x = 41
Alternative Hypothesis Hₐ x > 41
The test is a one-tail test
If significance level is 0.01 and n = 8 we need to use t-student distribution
From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1
df = 7 t(c) = 2.998
To calculate t(s) = ( x - 41 ) / s/√n
t(s) = ( 41.35 - 41 ) / 0.698/√8
t(s) = 0.35 * 2.83/ 0.698
t(s) = 1.419
Comparing t(s) and t(c)
t(s) < t(c)
t(s) is in the acceptance region we accept H₀
Answer:
Both get the same results that is,
![\left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
Given :
![\bf M=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]](https://tex.z-dn.net/?f=%5Cbf%20M%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
and initial population,
![\bf P=\left[\begin{array}{ccc}130\\300\\70\end{array}\right]](https://tex.z-dn.net/?f=%5Cbf%20P%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D130%5C%5C300%5C%5C70%5Cend%7Barray%7D%5Cright%5D)
a) - After two times, we will find in each position.
![P_2=[P].[M]^2=[P].[M].[M]](https://tex.z-dn.net/?f=P_2%3D%5BP%5D.%5BM%5D%5E2%3D%5BP%5D.%5BM%5D.%5BM%5D)
![M^2=\left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]\times \left[\begin{array}{ccc}\frac{1}{5}&\frac{1}{5}&\frac{2}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{1}{5}\\\frac{2}{5}&\frac{2}{5}&\frac{2}{5}\end{array}\right]](https://tex.z-dn.net/?f=M%5E2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B1%7D%7B5%7D%5C%5C%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%26%5Cfrac%7B2%7D%7B5%7D%5Cend%7Barray%7D%5Cright%5D)
![=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B25%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D)
![\therefore\;\;\;\;\;\;\;\;\;\;\;P_2=\left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right] \times\left[\begin{array}{ccc}130\\300\\70\end{array}\right] = \left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%5Ctherefore%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3B%5C%3BP_2%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D%20%5Ctimes%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D130%5C%5C300%5C%5C70%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
b) - With in migration process, 500 people are numbered. There will be after a long time,
![After\;inifinite\;period=[M]^n.[P]](https://tex.z-dn.net/?f=After%5C%3Binifinite%5C%3Bperiod%3D%5BM%5D%5En.%5BP%5D)
![Then,\;we\;get\;the\;same\;result\;if\;we\;measure [M]^n=\frac{1}{25} \left[\begin{array}{ccc}7&7&7\\8&8&8\\10&10&10\end{array}\right]](https://tex.z-dn.net/?f=Then%2C%5C%3Bwe%5C%3Bget%5C%3Bthe%5C%3Bsame%5C%3Bresult%5C%3Bif%5C%3Bwe%5C%3Bmeasure%20%5BM%5D%5En%3D%5Cfrac%7B1%7D%7B25%7D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%267%267%5C%5C8%268%268%5C%5C10%2610%2610%5Cend%7Barray%7D%5Cright%5D)
![=\left[\begin{array}{ccc}140\\160\\200\end{array}\right]](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D140%5C%5C160%5C%5C200%5Cend%7Barray%7D%5Cright%5D)
