Question

During a recent drought, a water utility in a certain town sampled 100 residential water bills and found that 80 of the residences had reduced their water consumption over that of the previous year. Find a 98% upper confidence bound for the proportion of residences that reduced their water consumption. Round the answer to three decimal places.

Answer 1

Answer: 0.893

Step-by-step explanation:

Given : Sample size of residential water bills: n=100

Number of residences had reduced their water consumption over that of the previous year = 80

Then sample proportion: $\hat{p}=\dfrac{80}{100}=0.8$

Critical value for 98% confidence= $z_{\alpha/2}=2.326$

The upper bound for confidence interval for population proportion :

$\hat{p}+ z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$=0.8+ (2.326)\sqrt{\dfrac{0.8(1-0.8)}{100}}\\\\=0.8+0.09304=0.89304\approx0.893$

Hence, the 98% upper confidence bound for the proportion of residences that reduced their water consumption.=0.893