Question

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 1

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 = 100

Sample proportion p = $\frac{73}{100} =0.73$

q = 1-p = 0.23

Std error of proportion = $\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.73*0.27}{100} } \\=0.04440$

95% Z critical value = 1.96

Margin of error = $1.96*0.0444 = 0.0870$

Confidence interval = sample proportion ±margin of error

0.642983946

0.817016054

(0.6430, 0.8170)