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Chapter 10: Q76 - Exercises (page 686)

Well water Trace metals found in wells affect the taste of drinking water, and high concentrations can pose a health risk. Researchers measured the concentration of zinc (in milligrams/liter) near the top and the bottom of 10 randomly selected wells in a large region. The data are provided in the following table.

a. Make a dot plot of the difference (Bottom鈥揟op) in the zinc concentrations for these 10 wells.

  1. Describe what the graph reveals about whether the amount of zinc at the top and bottom of the wells is the same, on average.

  2. Calculate the mean difference and the standard deviation of the differences. Interpret the mean difference.

Short Answer

Expert verified

Dot Plot graphically represents differences between tire and groove estimates, Maximum positive differences denote that major weight based estimates are higher than groove based estimates. Mean difference =0.0804,meanstandarddeviation=0.05227

Step by step solution

01

Dot Plot 

02

Interpretation 

The differences of zinc concentration between top and bottom levels of top wells

is positive in most of the sample units.

So, it states - zinc levels at the bottom of the well is more than zinc levels at the top of the well.

03

Mean and standard Deviation of Differences

MeanDifference=Sumofdifferences/Numberofdifferences=0.015+鈥�0.028+鈥�.....0.058+鈥�0.111=0.804/10=0.0804

StandardDeviation=鈭�(xi-x')2/(n-1)鈥�

where xi=eachdifference,x'=meandifference,n=numberofunits

  • 1st well : (xi-x')2=(0.015-0.0804)2=0.00427
  • 2nd well : (xi-x')2=0.028-0.0804=0.6021

Similarly finding all (xi-x')2and summing them,

[(0.015-0.0804)2+...+(0.111-0.0804)2]梅[10-1]=0.0245924/9=0.05227

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Most popular questions from this chapter

National Park rangers keep data on the bears that inhabit their park. Here is a histogram of the weights of bears measured in a recent year:

Which of the following statements is correct?

a. The median will lie in the interval (140,180), and the mean will lie in the interval(180,220).

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d. The mean will lie in the interval (140,180),and the median will lie in the interval (260,300).

e. The mean will lie in the interval (100,140), and the median will lie in the interval (180,220).

Which of the following describes a Type II error in the context of this study?

a. Finding convincing evidence that the true means are different for males and females when in reality the true means are the same

b. Finding convincing evidence that the true means are different for males and females when in reality the true means are different

c. Not finding convincing evidence that the true means are different for males and females when in reality the true means are the same

d. Not finding convincing evidence that the true means are different for males and females when in reality the true means are different

e. Not finding convincing evidence that the true means are different for males and females when in reality there is convincing evidence that the true means are different.

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