Answer:
The 95% CI for the difference of means is:
![-155.45 \leq \mu_1-\mu_2 \leq -44.55](https://tex.z-dn.net/?f=-155.45%20%5Cleq%20%5Cmu_1-%5Cmu_2%20%5Cleq%20-44.55)
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>"Find a 95% confidence interval on the difference of the towels mean absorbency produced by the two processes. Assumed that the standard deviations are estimated from the data. Round to two decimals places."</em>
Process 1:
- Sample size: 10
- Mean: 200
- S.D.: 15
Process 2:
- Sample size: 4
- Mean: 300
- S.D.: 50
The difference of the sample means is:
![M_d=M_1-M_2=200-300=-100](https://tex.z-dn.net/?f=M_d%3DM_1-M_2%3D200-300%3D-100)
The standard deviation can be estimated as:
![\sigma_d=\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}\\\\\sigma_d=\sqrt{\frac{15^2}{10}+\frac{50^2}{4}} =\sqrt{22.5+625}=\sqrt{647.5}=25.45](https://tex.z-dn.net/?f=%5Csigma_d%3D%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%5C%5C%5C%5C%5Csigma_d%3D%5Csqrt%7B%5Cfrac%7B15%5E2%7D%7B10%7D%2B%5Cfrac%7B50%5E2%7D%7B4%7D%7D%20%3D%5Csqrt%7B22.5%2B625%7D%3D%5Csqrt%7B647.5%7D%3D25.45)
The degrees of freedom are:
![df=n_1+n_2-2=10+4-2=12](https://tex.z-dn.net/?f=df%3Dn_1%2Bn_2-2%3D10%2B4-2%3D12)
The t-value for a 95% confidence interval and 12 degrees of freedom is t=±2.179.
Then, the confidence interval can be written as:
![M_d-t\cdot \sigma_d\leq \mu_1-\mu_2 \leq M_d+t\cdot \sigma_d\\\\-100-2.179*25.45\leq \mu_1-\mu_2 \leq -100+2.179*25.45\\\\-100-55.45 \leq \mu_1-\mu_2 \leq -100+55.45\\\\ -155.45 \leq \mu_1-\mu_2 \leq -44.55](https://tex.z-dn.net/?f=M_d-t%5Ccdot%20%5Csigma_d%5Cleq%20%5Cmu_1-%5Cmu_2%20%5Cleq%20M_d%2Bt%5Ccdot%20%5Csigma_d%5C%5C%5C%5C-100-2.179%2A25.45%5Cleq%20%5Cmu_1-%5Cmu_2%20%5Cleq%20-100%2B2.179%2A25.45%5C%5C%5C%5C-100-55.45%20%5Cleq%20%5Cmu_1-%5Cmu_2%20%5Cleq%20-100%2B55.45%5C%5C%5C%5C%20-155.45%20%5Cleq%20%5Cmu_1-%5Cmu_2%20%5Cleq%20-44.55)
Answer:
Interior: 135 degrees
Exterior: 45 degrees
Step-by-step explanation:
The interior angle of a regular octagon is exactly 135 degrees, which can be found using the (n – 2)180 formula. The exterior is simply 180 - the interior, which is 45. :)
Answer:
15 people are able to be at the charity gala because 77:55 divided by 5:17.
Answer: 17000000 ounces of gold were mined in that country that year.
Step-by-step explanation:
Let x represent the number of ounces of gold that were mined in that country that year.
Approximately 1,870,000 oz of gold went into the manufacturing of electronic equipment in a certain country in 1 year. This was 11% of all the gold mined in that country that year. This means that
11/100 × x = 1870000
0.11x = 1870000
x = 1870000/0.11
x = 17000000