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Magazine Chapter 6: Q116SE (page 375)
Lead and copper in drinking water. Periodically, the Hillsborough County (Florida) Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead and copper levels in water specimens collected for a sample of 10 residents of the Crystal Lakes Manors subdivision are shown below, followed by a Minitab printout analysing the data.
a. Locate a 90% confidence interval for the mean lead level in water specimens from Crystal Lakes Manors on the printout.
b. Locate a 90% confidence interval on the printout for the mean copper level in water specimens from Crystal Lakes Manors.
c. Interpret the intervals, parts a and b, in the words of the problem.
d. Discuss the meaning of the phrase 鈥�90% confident.鈥�
Short Answer
- From the Minitab output, the 90% confidence interval for the mean lead in water specimen from Crystal Lakes Manors is (0.61,5.16).
- From the Minitab output, the 90% confidence interval for the mean copper level in water specimen from Crystal Lakes Manors is (0.2637, 0.5529).
- It is 90% confident that the true mean lead level in water specimens from Crystal Lakes Manors lies in between 0.61 and 5.16. It can conclude that 90% are confident that the true mean lead level in water specimens from Crystal Lakes Manors lies in between 0.2637 and 0.5529.
- The phrase 鈥�90% confident鈥� indicates that 90% of all similarly constructed intervals contain the true mean.
Step by step solution
Given information
The lead and copper levels in water specimens collected for a sample of 10 residents of the Crystal Lakes Manors subdivision are given as follows:
Also, the Minitab output is given as:
(a) Finding the 90% confidence interval for the mean lead level in the water
From the Minitab output, the 90% confidence interval for the mean lead in water specimen from Crystal Lakes Manors is (0.61,5.16). It is 90% confident that the mean lead in the water specimen lies between 0.61 mg/l and 5.16 mg/l.
(b) Finding the 90% confidence interval for the mean copper level in the water
From the Minitab output, the 90% confidence interval for the mean copper level in water specimen from Crystal Lakes Manors is (0.2637, 0.5529). It is 90% confident that the mean copper level in the water specimen lies between 0.2637 mg/l and 0.5529 mg/l.
(c) Interpretation of the confidence interval for the mean lead level and mean copper level in the water
It is 90% confident that the true mean lead level in water specimens from Crystal Lakes Manors lies in between 0.61 and 5.16. It can conclude that 90% are confident that the true mean lead level in water specimens from Crystal Lakes Manors lies in between 0.2637 and 0.5529.
(d) Meaning of “90% confident”
The phrase 鈥�90% confident鈥� indicates that 90% of all similarly constructed intervals contain the true mean.
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