Answer: 95% confidence interval for the difference between the proportions would be (1.31, 1.39).
Step-by-step explanation:
Since we have given that
Number of alluvial wells = 349
Number of quaternary wells = 143
Number of alluvial wells that had concentrations above 0.1 = 182
Number of quaternary wells that had concentrations above 0.1 = 112
Average of alluvial wells = 0.27
Standard deviation = 0.4
Average of quaternary wells = 1.62
Standard deviation =1.70
So, 95% confidence interval gives
alpha = 5% level of significance.
![\dfrac{\alpha}{2}=2.5\%\\\\z_{\frac{\alpha}{2}}=1.96](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Calpha%7D%7B2%7D%3D2.5%5C%25%5C%5C%5C%5Cz_%7B%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3D1.96)
So, 95% confidence interval becomes,
![(1.62-0.27)\pm 1.96\sqrt{\dfrac{0.4^2}{349}+\dfrac{1.7^2}{143}}\\\\=1.35\pm 1.96\times 0.020\\\\=(1.35-0.040,1.35+0.040)\\\\=(1.31,1.39)](https://tex.z-dn.net/?f=%281.62-0.27%29%5Cpm%201.96%5Csqrt%7B%5Cdfrac%7B0.4%5E2%7D%7B349%7D%2B%5Cdfrac%7B1.7%5E2%7D%7B143%7D%7D%5C%5C%5C%5C%3D1.35%5Cpm%201.96%5Ctimes%200.020%5C%5C%5C%5C%3D%281.35-0.040%2C1.35%2B0.040%29%5C%5C%5C%5C%3D%281.31%2C1.39%29)
Hence, 95% confidence interval for the difference between the proportions would be (1.31, 1.39).