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

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}=(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{\frac{\hat{p}(1-\hat{p})}{n}}`

`=0.8+ (2.326)\sqrt{(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