Hey There! Whoever we see the keyword “of”, we know that it’s multiplication Therefore we’re multiplying 1/3 and 7/1 that gives us 7/3
Answer:
99% CI:
![-4.637\leq\mu_v-\mu_o\leq 3.737](https://tex.z-dn.net/?f=-4.637%5Cleq%5Cmu_v-%5Cmu_o%5Cleq%203.737)
Step-by-step explanation:
We have to calculate a 99%CI for the difference of means for the vegan and the omnivore.
First, we have to estimate the standard deviation
![s_{Md}=\sqrt{\frac{2MSE}{n_h}}](https://tex.z-dn.net/?f=s_%7BMd%7D%3D%5Csqrt%7B%5Cfrac%7B2MSE%7D%7Bn_h%7D%7D)
The MSE can be calculated as
![MSE=\frac{(SSE_1+SSE_2)}{df} =\frac{(n_1s_1)^2+(n_2*s_2)^2}{n_1+n_2-2}\\\\MSE=\frac{(85*1.05)^2+(96*1.20)^2}{85+96-2}=\frac{7965.56+13272.04}{179} =118.65](https://tex.z-dn.net/?f=MSE%3D%5Cfrac%7B%28SSE_1%2BSSE_2%29%7D%7Bdf%7D%20%3D%5Cfrac%7B%28n_1s_1%29%5E2%2B%28n_2%2As_2%29%5E2%7D%7Bn_1%2Bn_2-2%7D%5C%5C%5C%5CMSE%3D%5Cfrac%7B%2885%2A1.05%29%5E2%2B%2896%2A1.20%29%5E2%7D%7B85%2B96-2%7D%3D%5Cfrac%7B7965.56%2B13272.04%7D%7B179%7D%20%3D118.65)
The weighted sample size nh can be calculated as
![n_h=\frac{2}{1/n_1+1/n_2}=\frac{2}{1/85+1/96}=\frac{2}{0.0222} =90.16](https://tex.z-dn.net/?f=n_h%3D%5Cfrac%7B2%7D%7B1%2Fn_1%2B1%2Fn_2%7D%3D%5Cfrac%7B2%7D%7B1%2F85%2B1%2F96%7D%3D%5Cfrac%7B2%7D%7B0.0222%7D%20%3D90.16)
The standard deviation then becomes
![s_{Md}=\sqrt{\frac{2MSE}{n_h}}=\sqrt{\frac{2*118.65}{90.16}}=\sqrt{2.632} =1.623](https://tex.z-dn.net/?f=s_%7BMd%7D%3D%5Csqrt%7B%5Cfrac%7B2MSE%7D%7Bn_h%7D%7D%3D%5Csqrt%7B%5Cfrac%7B2%2A118.65%7D%7B90.16%7D%7D%3D%5Csqrt%7B2.632%7D%20%3D1.623)
The z-value for a 99% confidence interval is z=2.58.
The difference between means is
![\Delta M=M_v-M_o=5.10-5.55=-0.45](https://tex.z-dn.net/?f=%5CDelta%20M%3DM_v-M_o%3D5.10-5.55%3D-0.45)
Then the confidence interval can be constructed as
![\Delta M-z*s_{Md}\leq\mu_v-\mu_o\leq \Delta M+z*s_{Md}\\\\ -0.45-2.58*1.623\leq\mu_v-\mu_o\leq -0.450+2.58*1.623\\\\-0.450-4.187\leq\mu_v-\mu_o\leq-0.450+4.187\\\\-4.637\leq\mu_v-\mu_o\leq 3.737](https://tex.z-dn.net/?f=%5CDelta%20M-z%2As_%7BMd%7D%5Cleq%5Cmu_v-%5Cmu_o%5Cleq%20%5CDelta%20M%2Bz%2As_%7BMd%7D%5C%5C%5C%5C%20-0.45-2.58%2A1.623%5Cleq%5Cmu_v-%5Cmu_o%5Cleq%20-0.450%2B2.58%2A1.623%5C%5C%5C%5C-0.450-4.187%5Cleq%5Cmu_v-%5Cmu_o%5Cleq-0.450%2B4.187%5C%5C%5C%5C-4.637%5Cleq%5Cmu_v-%5Cmu_o%5Cleq%203.737)
That means the thousands number will either be the same or 1 higher based on the hundreds place & everything after the thousands place will be 0s
247,000
Answer:
0, -2/3
Step-by-step explanation: