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 71.97% 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?