Answer
test statistic
P-value ![p- value = 0.0198](https://tex.z-dn.net/?f=p-%20value%20%20%3D%20%200.0198)
Step-by-step explanation:
From the question we are told that
The first sample size is ![n_1 = 5](https://tex.z-dn.net/?f=n_1%20%20%3D%205)
The first sample mean is ![\= x_1 = 1.76 \ mm](https://tex.z-dn.net/?f=%5C%3D%20x_1%20%20%3D%20%201.76%20%5C%20mm)
The first standard is ![s_1 = 0.55](https://tex.z-dn.net/?f=s_1%20%20%20%3D%20%200.55)
The second is ![sample \ size\ is\ n_2 = 11](https://tex.z-dn.net/?f=sample%20%5C%20size%5C%20is%5C%20%20n_2%20%3D%20%2011)
The second sample mean is ![\= x_2 = 2.56](https://tex.z-dn.net/?f=%5C%3D%20x_2%20%20%20%3D%202.56)
The second standard deviation is ![\sigma = 0.84](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%200.84)
The level of significance is ![\alpha = 0.01](https://tex.z-dn.net/?f=%5Calpha%20%20%3D%20%200.01)
The null hypothesis is ![H_o : \mu_1 - \mu_2 = 0](https://tex.z-dn.net/?f=H_o%20%3A%20%20%5Cmu_1%20-%20%5Cmu_2%20%3D%200)
The alternative hypothesis is ![H_a: \mu_1 - \mu_2 < 0](https://tex.z-dn.net/?f=H_a%3A%20%5Cmu_1%20-%20%5Cmu_2%20%3C%20%200)
Generally the test statistics is mathematically represented as
![t = \frac{ (\= x _1 - \= x_2) - ( \mu_1 - \mu_2)}{ \sqrt{\frac{s_1 ^2 }{ n_1 } + \frac{s_1 ^2 }{ n_1 } } }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B%20%28%5C%3D%20x%20_1%20-%20%5C%3D%20x_2%29%20-%20%28%20%5Cmu_1%20-%20%5Cmu_2%29%7D%7B%20%5Csqrt%7B%5Cfrac%7Bs_1%20%5E2%20%7D%7B%20n_1%20%7D%20%20%2B%20%5Cfrac%7Bs_1%20%5E2%20%7D%7B%20n_1%20%7D%20%20%7D%20%7D)
=> ![t = \frac{ (1.76 - 2.56 ) - 0 }{ \sqrt{\frac{0.55^2 }{ 5 } + \frac{0.84^2 }{11 } } }](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7B%20%281.76%20-%202.56%20%29%20-%200%20%7D%7B%20%5Csqrt%7B%5Cfrac%7B0.55%5E2%20%7D%7B%205%20%7D%20%20%2B%20%5Cfrac%7B0.84%5E2%20%7D%7B11%20%7D%20%20%7D%20%7D)
=>
Generally degree of freedom is mathematically represented as
![df = n_1 + n_2 - 2](https://tex.z-dn.net/?f=df%20%20%3D%20n_1%20%2B%20n_2%20-%202)
=> ![df = 5 + 11 - 2](https://tex.z-dn.net/?f=df%20%20%3D%205%20%2B%2011%20-%202)
=> ![df = 14](https://tex.z-dn.net/?f=df%20%20%3D%2014)
From the student t distribution table the probability value to the left that corresponds to
at a degree of freedom of
is
![p- value = 0.0198](https://tex.z-dn.net/?f=p-%20value%20%20%3D%20%200.0198)
Answer: -80
Step-by-step explanation:
Answer: 5000000
Step-by-step explanation:
0.55 x 1
975 = 5000000
253 oz
............................
There are 8 people, but only 2 pies. So to figure out how much each person gets when divided, which is a keyword, equally. So to put it in fraction form it would be 2/8. If you simplify it you get 1/4. In decimal form, 2/8 and 1/4 both equal 0.25. Hope this helps you to understand it a bit more!