Answer:
![\frac{1}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B10%7D)
Step-by-step explanation:
![m-6(n+2)=-8\\6n+m=16](https://tex.z-dn.net/?f=m-6%28n%2B2%29%3D-8%5C%5C6n%2Bm%3D16)
Rearrange the second equation and substitute it into the first equation.
![m=16-6n\\16-6n-6(n+2)=-8\\16-6n-6n-12=-8\\16-12n-12=-8\\4-12n=-8\\4+8=12n\\12=12n\\n=1](https://tex.z-dn.net/?f=m%3D16-6n%5C%5C16-6n-6%28n%2B2%29%3D-8%5C%5C16-6n-6n-12%3D-8%5C%5C16-12n-12%3D-8%5C%5C4-12n%3D-8%5C%5C4%2B8%3D12n%5C%5C12%3D12n%5C%5Cn%3D1)
Now we can use our value of n, and substitute it into the second equation to solve for m.
![6(1)+m=16\\6+m=16\\m=10](https://tex.z-dn.net/?f=6%281%29%2Bm%3D16%5C%5C6%2Bm%3D16%5C%5Cm%3D10)
Now we can divide our values.
![\frac{n}{m}=\frac{1}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Bn%7D%7Bm%7D%3D%5Cfrac%7B1%7D%7B10%7D)
Answer:
Follows are the solution to this question:
Step-by-step explanation:
Please find the complete question in the attachment file.
![n_1 = 26 \\\\ x_1 = 16.12 \\\\s_1 = 3.58\\\\n_2 = 26\\\\ x_2 = 19.85 \\\\ s_2 = 4.51](https://tex.z-dn.net/?f=n_1%20%3D%2026%20%5C%5C%5C%5C%20x_1%20%3D%2016.12%20%5C%5C%5C%5Cs_1%20%3D%203.58%5C%5C%5C%5Cn_2%20%3D%2026%5C%5C%5C%5C%20x_2%20%3D%2019.85%20%5C%5C%5C%5C%20s_2%20%3D%204.51)
![H_0: u_1 = u_2\\\\H_1: u_1 \neq u_2](https://tex.z-dn.net/?f=H_0%3A%20u_1%20%3D%20u_2%5C%5C%5C%5CH_1%3A%20u_1%20%5Cneq%20u_2)
Using formula:
![\to S^{2}_{p}=\frac{S^{2}_{1}(n_1 -1)+ S^{2}_{2}(n_2-1)}{n_1+n_2-2}](https://tex.z-dn.net/?f=%5Cto%20S%5E%7B2%7D_%7Bp%7D%3D%5Cfrac%7BS%5E%7B2%7D_%7B1%7D%28n_1%20-1%29%2B%20S%5E%7B2%7D_%7B2%7D%28n_2-1%29%7D%7Bn_1%2Bn_2-2%7D)
![\to Sp^2 = \frac{((26-1) \times (3.58^2) + (26-1) \times (4.51^2))}{(26+26-2)}](https://tex.z-dn.net/?f=%5Cto%20Sp%5E2%20%3D%20%5Cfrac%7B%28%2826-1%29%20%5Ctimes%20%283.58%5E2%29%20%2B%20%2826-1%29%20%5Ctimes%20%284.51%5E2%29%29%7D%7B%2826%2B26-2%29%7D)
![= \frac{((25) \times 12.8164 + (25) \times 20.3401 )}{(26+24)}\\\\ = \frac{(320.41 + 508.5025)}{(50)}\\\\ = \frac{(828.9125)}{(50)}\\\\=16.57825](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%28%2825%29%20%5Ctimes%2012.8164%20%2B%20%2825%29%20%5Ctimes%2020.3401%20%29%7D%7B%2826%2B24%29%7D%5C%5C%5C%5C%20%3D%20%5Cfrac%7B%28320.41%20%2B%20508.5025%29%7D%7B%2850%29%7D%5C%5C%5C%5C%20%3D%20%5Cfrac%7B%28828.9125%29%7D%7B%2850%29%7D%5C%5C%5C%5C%3D16.57825)
![\to Sp = 4.0716](https://tex.z-dn.net/?f=%5Cto%20Sp%20%3D%204.0716)
Calculating the value of standard error:
![\to SE = Sp \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}](https://tex.z-dn.net/?f=%5Cto%20SE%20%3D%20Sp%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B1%7D%7Bn_1%7D%2B%5Cfrac%7B1%7D%7Bn_2%7D%7D)
![=4.0716 \times \sqrt{\frac{1}{26}+\frac{1}{26}}\\\\=4.0716 \times \sqrt{\frac{1+1}{26}}\\\\=4.0716 \times \sqrt{\frac{2}{26}}\\\\=4.0716 \times \sqrt{\frac{1}{13}}\\\\=4.0716 \times 0.277 \\\\=1.1278332\\\\= 1.1293](https://tex.z-dn.net/?f=%3D4.0716%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B1%7D%7B26%7D%2B%5Cfrac%7B1%7D%7B26%7D%7D%5C%5C%5C%5C%3D4.0716%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B1%2B1%7D%7B26%7D%7D%5C%5C%5C%5C%3D4.0716%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B2%7D%7B26%7D%7D%5C%5C%5C%5C%3D4.0716%20%5Ctimes%20%5Csqrt%7B%5Cfrac%7B1%7D%7B13%7D%7D%5C%5C%5C%5C%3D4.0716%20%5Ctimes%200.277%20%5C%5C%5C%5C%3D1.1278332%5C%5C%5C%5C%3D%201.1293)
Calculating the value of test statistic:
Formula:
![\to t = \frac{(x_1-x_2)}{SE}](https://tex.z-dn.net/?f=%5Cto%20t%20%3D%20%5Cfrac%7B%28x_1-x_2%29%7D%7BSE%7D)
![= \frac{(16.12 -19.85)}{1.1293}\\\\= \frac{(-3.73)}{1.1293}\\\\=-3.303](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%2816.12%20-19.85%29%7D%7B1.1293%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B%28-3.73%29%7D%7B1.1293%7D%5C%5C%5C%5C%3D-3.303)
Calculating the value of Degree of freedom:
![= n_1+n_2 -2 \\\\= 26+26 -2 \\\\= 52 -2 \\\\= 50](https://tex.z-dn.net/?f=%3D%20n_1%2Bn_2%20-2%20%5C%5C%5C%5C%3D%2026%2B26%20-2%20%5C%5C%5C%5C%3D%2052%20-2%20%5C%5C%5C%5C%3D%2050)
Because the P-value is a 2-tailed test = 0.0018
Thus they reject H0, because of P-value < 0.05,
Yeah, certain data show clearly that the means are different.
Answer:
x= -10
Step-by-step explanation: