before the hurricanes, the soils on New Orleans.... Part B. and C. please WITHOU

Question

before the hurricanes, the soils on New Orleans....
Part B. and C. please WITHOUT using minitab.
Thank you

Assignment Problems 323 t was ricanes, the soils in New Orleans were known to have high concentrations of lead, which is a dangerous environmental toxin. Forty-six sites had been monitored before the hurricanes for soil lead content, as measured in mg/kg, and the soil from each of these sites was measured again after the hurricanes (Zahran et al. 2010). The data given below show the log of the ratio of the soil lead content after the hurricanes and the soil lead content before the hurricanes-we'll call this variable the "change in soil lead." (There- fore, numbers less than zero show a reduction in soil lead content after the hurricanes, and num- ers greater than zero show increases.) This log ratio has an approximately normal distribution n was -0.83,-0.18, 0.14,-1.46, -0.48, -1.04, 0.25, -0.34,-0.81,-0.83, -0.60, 0.34,-0.75, 0.37, -u22 0.26, 0.46,-0.03,-0.32,-0.53,-1.55,-0.90, -0.95,-0.13,-0.75, 0.59,-0.06, 0.39,-0.40,-3,2 -0.84,-0.56, 0.44, 0.18, 0.28,-0.41,-0.26, 0.64,-0.51,-0.36, 0.49, 0.21, 0.17, 0.13, -0.63, -1.24, 0.57,-0.782.48 a. Draw a graph of the data, following recom- mended principles of good graph design (Chapter 2). What trend is suggested? b. Determine the most-plausible range of values for the mean change in soil lead. Describe in words what the nature of that change is. Is arn increase in soil lead consistent with the data? Is a decrease in soil lead consistent? Test whether mean soil lead changed after the hurricanes. er c. 22. Refer to Assignment Problem 21. In the same

Explanation / Answer

Solution

Part (b)

Let X = change in soil lead [i.e., log of the ratio of the soil lead content after and before hurricanes.]

We are given that X follows an approximate Normal Distribution, say X ~ N(µ, 2), where µ = mean NS = standard deviation

And we have to find the most plausible range of values for the mean change in soil lead.

This is nothing but the Confidence Interval (CI) for µ and we will take 95% CI as the most plausible.

Back-up Theory   

100(1 - )% CI for µ is given by: {Xbar ± (s/n)(t/2)}, where

Xbar = sample mean, s = sample standard deviation, n = sample size and t/2 = upper /2 % point of t-distribution with degrees of freedom = (n - 1).

Calculations

Summary of Excel calculations is given below:

=

0.05

n =

46

             

Xbar =

-0.274782609

s =

0.577545531

             tn-1, /2 =

2.014103359

95% CI for

-0.274782609

±

0.171509849

Lower Bound =

-0.44629246

Upper Bound =

-0.10327276

ANSWER 1

Since both bounds are negative,

the nature of change is a reduction in soil lead content. ANSWER 2

Part (c)

Testing for change in mean soil lead

We test for µ = 0.

Since the 95% CI does not contain zero, the hypothesis µ = 0 is rejected at 5% level of significance.

This implies that change in mean soil lead is a reduction.

i.e., hurricanes reduce the lead level in soil.

DONE

=

0.05

n =

46

             

Xbar =

-0.274782609

s =

0.577545531

             tn-1, /2 =

2.014103359

95% CI for

-0.274782609

±

0.171509849

Lower Bound =

-0.44629246

Upper Bound =

-0.10327276

ANSWER 1

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