During a recent drought, a water utility in a certain town sampled 100 residential water bills and found out that 73 of the residences had reduced their water consumption over that of the previous year. Find a 95% confidence interval for the proportion of residences that reduced their water

Answer:(0.6430, 0.8170)Step-by-step explanation:Given that during a recent drought a water utility in a certain town sampled 100 residential water bills and found out that 73 of the residences had reduced their water consumption over that of the previous year. Sample size n = 100Sample proportion p = [tex]\frac{73}{100} =0.73[/tex]q = 1-p = 0.23Std error of proportion = [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.73*0.27}{100} } \\=0.04440[/tex]95% Z critical value = 1.96Margin of error = [tex]1.96*0.0444 = 0.0870[/tex]Confidence interval = sample proportion ±margin of error0.642983946 0.817016054 (0.6430, 0.8170)