Question

In: Statistics and Probability

During a recent drought, a water utility in a certain town sampled 100 residential water bills...

During a recent drought, a water utility in a certain town sampled 100 residential water bills and found that 79 of the residences had reduced their water consumption over that of the previous year.

A) Find a 95% confidence interval for the proportion of residences that reduced their water consumption. Round the answers to three decimal places.

B) Find a 99% confidence interval for the proportion of residences that reduced their water consumption. Round the answers to three decimal places.

Solutions

Expert Solution

Sample proportion = 79 / 100 = 0.79

a)

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n] < p < + Z/2 * sqrt [ ( 1 - ) / n]

0.79 - 1.96 * sqrt [ 0.79 ( 1 - 0.79) / 100] < p < 0.79 + 1.96 * sqrt [ 0.79 ( 1 - 0.79) / 100]

0.710 < p < 0.870

95% CI is ( 0.710 , 0.870 )

b)

99% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n] < p < + Z/2 * sqrt [ ( 1 - ) / n]

0.79 - 2.5758 * sqrt [ 0.79 ( 1 - 0.79) / 100] < p < 0.79 + 2.5758 * sqrt [ 0.79 ( 1 - 0.79) / 100]

0.685 < p < 0.895

99% CI is ( 0.685 , 0.895 )

orchestra answered 2 years ago
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