During a recent drought, a water utility in a certain town sampled 100 residential water billsand found that 73 of the residences had reduced their water consumption over that of theprevious year.a) Find a 95% confidence interval for the proportion of residences that reduced theirwater consumption.b) Find a 99% confidence interval for the proportion of residences that reduced their water consumption. c) Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05. d) Find the sample size needed for a 99% confidence interval to specify the proportion to within ±0.05. e) Someone claims that more than 70% of residences reduced their water consumption. With what level of confidence can this statement be made? f) If 95% confidence intervals are computed for 200 towns, what is the probability that more than 192 of the confidence intervals cover the true proportions?
During a recent drought, a water utility in a certain town sampled 100 residential water bills
and found that 73 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.
b) Find a 99% confidence interval for the proportion of residences that reduced their water consumption. c) Find the sample size needed for a 95% confidence interval to specify the proportion to
within ±0.05.
d) Find the sample size needed for a 99% confidence interval to specify the proportion to
within ±0.05.
e) Someone claims that more than 70% of residences reduced their water consumption.
With what level of confidence can this statement be made?
f) If 95% confidence intervals are computed for 200 towns, what is the probability that
more than 192 of the confidence intervals cover the true proportions?
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