Problem 2E

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?

Solution:

Step 1 of 5:

The water utility in a certain town samples 100 residential water bills and found that 73 of the residence are reduced their water consumption over that of previous year.

We have to find

- The 95% CI for the proportion of residences that reduce their water consumption.
- The 99% CI for the proportion of residences that reduce their water consumption.
- The sample size needed for a 95% CI to specify the proportion within .
- The sample size needed for a 99% CI to specify the proportion within .
- At what level of confidence the claim that more than 70% of the residences reduce their water content.
- The probability that more than 192 of the confidence intervals cover the true proportion.