Answer:
0.5
Step-by-step explanation:
vertex point formula= -b/2a
3x-3+2
3/6=0.5
<span> x + 1
/
3x • (x - 10)<span>2</span></span>
(x-3)^2+(y-2)^2=25
plug in those values for x,y to see if they satisfy the equation (=25)
Given :
Number of methods, k = 3
Number of the observations, n = 30
Degrees of freedom Treatment = k - 1
= 3 - 1 = 2
Degrees of freedom for error = n - k
= 30 - 3 = 27
![$SSTR = 4560, \ SST = 10800$](https://tex.z-dn.net/?f=%24SSTR%20%3D%204560%2C%20%5C%20SST%20%3D%2010800%24)
![$SSE = SST - SSTR$](https://tex.z-dn.net/?f=%24SSE%20%3D%20SST%20-%20SSTR%24)
= 10800 - 4560
= 6240
![$SSE_{treatment} = MS_{treatment } \times DF_{treatment}$](https://tex.z-dn.net/?f=%24SSE_%7Btreatment%7D%20%3D%20MS_%7Btreatment%20%7D%20%5Ctimes%20DF_%7Btreatment%7D%24)
![$MS_{treatment} = \frac{4560}{2}=2280$](https://tex.z-dn.net/?f=%24MS_%7Btreatment%7D%20%3D%20%5Cfrac%7B4560%7D%7B2%7D%3D2280%24)
![$MS_{error}=\frac{SSE_{error}}{DF_{error}}$](https://tex.z-dn.net/?f=%24MS_%7Berror%7D%3D%5Cfrac%7BSSE_%7Berror%7D%7D%7BDF_%7Berror%7D%7D%24)
![$=\frac{6240}{27}=231.1$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B6240%7D%7B27%7D%3D231.1%24)
![$F=\frac{MS_{treatment}}{MS_{error}}$](https://tex.z-dn.net/?f=%24F%3D%5Cfrac%7BMS_%7Btreatment%7D%7D%7BMS_%7Berror%7D%7D%24)
![$=\frac{2280}{231.1}=9.865$](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B2280%7D%7B231.1%7D%3D9.865%24)
Source variation Sum of square Degrees of freedom Mean square F
Treatment 4560 2 2280 9.8653
Error 6240 27 231.11111111
Total 10800
The critical value of F for the 0.05 sig level and df (227) is 3.354
Since the test stat > critical value of F, so we reject null hypothesis and state that there is a significant difference in the means of the three assembly methods.