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Natalija [7]
3 years ago
6

During a recent drought, a water utility in a certain town sampled 100 residential water bills and found out that 73 of the resi

dences 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
Mathematics
1 answer:
ankoles [38]3 years ago
4 0

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)

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