The correct answer is the first choice, ($1818.30, $5077.70.)
To find this, we first find the z-score based on the confidence level:
Convert 95% to a decimal: 95%=95/100 = 0.95
Subtract from 1: 1-0.95 = 0.05
Divide by 2: 0.05/2 = 0.025
Subtract from 1: 1-0.025 = 0.975
Using a z-table (http://www.z-table.com) we see that this value is associated with a z-score of 1.96.
Next, we identify
![\overline{x_1}=39902; \overline{x_2}=36454; n_1=74; n_2=40; \sigma_1=3270; \sigma_2=4677](https://tex.z-dn.net/?f=%5Coverline%7Bx_1%7D%3D39902%3B%20%5Coverline%7Bx_2%7D%3D36454%3B%20n_1%3D74%3B%20n_2%3D40%3B%20%5Csigma_1%3D3270%3B%20%5Csigma_2%3D4677)
Next we find
![(\overline{x_1}-\overline{x_2})=(39902-36454) = 3448](https://tex.z-dn.net/?f=%28%5Coverline%7Bx_1%7D-%5Coverline%7Bx_2%7D%29%3D%2839902-36454%29%20%3D%203448)
Next we find
![\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}} \\ \\=\sqrt{\frac{3270^2}{74}+\frac{4677^2}{40}}=\sqrt{\frac{10692900}{74}+\frac{21874329}{40}} \\ \\=831.479](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B%5Csigma_1%5E2%7D%7Bn_1%7D%2B%5Cfrac%7B%5Csigma_2%5E2%7D%7Bn_2%7D%7D%0A%5C%5C%0A%5C%5C%3D%5Csqrt%7B%5Cfrac%7B3270%5E2%7D%7B74%7D%2B%5Cfrac%7B4677%5E2%7D%7B40%7D%7D%3D%5Csqrt%7B%5Cfrac%7B10692900%7D%7B74%7D%2B%5Cfrac%7B21874329%7D%7B40%7D%7D%0A%5C%5C%0A%5C%5C%3D831.479)
Next, we multiply this value by z:
1.96(831.479) = 1629.70
The confidence interval is given by
Answer: It is C
Step-by-step explanation: