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Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.2 - Problem 2e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 5.2 - Problem 2e

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# During a recent drought, a water utility in a certain town

ISBN: 9780073401331 38

## Solution for problem 2E Chapter 5.2

Statistics for Engineers and Scientists | 4th Edition

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Problem 2E

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?

Step-by-Step Solution:

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

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

Step 2 of 3

Step 3 of 3

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During a recent drought, a water utility in a certain town