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27.12.2020 •
Mathematics
A County Water Department tested the drinking water of randomly selected 10 homeowners for lead and copper contamination. The test results yielded sample mean and sample standard deviation for lead as 2.89 and 3.92 (in µg/L), respectively, and for copper as 0.4083 and 0.2495 (in mg/L), respectively. a) Set up 90% confidence interval for the mean lead level in drinking water in that county and interpret the result. (3 Points) b) Set up 90% confidence interval for the mean copper level in drinking water in that county and interpret the result. (3 Points) c) What are the underlying assumptions? (1 Point)
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Ответ:
a. (0.6178, 5.1622)
b. (0.2637, 0.5592)
c.
Step-by-step explanation:
A.
For lead
n1 = 10
X1 = 2.89
S1 = 3.92
90% ci = 1-90%
= 0.10
TCritical = 1.833
Degree of freedom = 10-1 = 9
X1 +- TCritical * s/√n
= 2.88 +-1.833x3.92/√10
= 2.89+-2.2722
= 0.6178, 5.1622
Lead in water lies between this interval at 90% confidence level.
For cooper
n2 = 10
X2 = 0.4083
S2 = 0.2495
Alpha = 0.10
Df = 9
TCritical = 1.833
0.4083+-1.833*9.2495/√10
= 0.4084+-0.14462
= (0.26368, 0.55292)
Copper in water lies between this interval at 90% confidence level
C.
Underlying assumptions
The samples are randomly taken as well as independent. The sample size is not big enough. So it is approximately normally distributed.
Ответ:
A. The weight of the objects inside the box