Question

Please completely answer the below Biostatistic question.

Hurricanes Rita and Katrina caused flooding of large parts of New Orleans, leaving behind large amounts of new sediment. Before the hurricanes, the soils of New Oleans were known to have high concentrations of lead, a dangerous toxin capable of creating potential health hazard. Zaharan et al. (2010) were interested in the human health impacts of the flood and so measured lead concentrations of blood (in ug/dl) of children who lived in 46 different affected areas both before and after the floods. Complete the responses for the following R outputs.

R Output

data: lead$bloodLeadAfter and lead$bloodLeadBefore

t = -8.031, df = 45, p-value = 3.107e-10

alternative hypothesis: truedifference in means is not equal to 0

95% confidence interval: -2.411851 -1.444671

sample estimates: mean of the differences = -1.928261

a.) Name the sampling unit and sample size

b.) Name the variable(s) and associated scale(s)

c.) Name the design (one-sample t-test, two-sample t-test, paired t-test)

d.) Is this an appropriate design, given the narrative above? Why or why not?

e.) Name the population parameter of interest, using specific descriptors from the narrative (hint: write what are we estimating in specific terms)

f.) Use the output to write the null hypothesis for the associated t-test (be sure to state it in terms of the population parameter of interest)

g.) Use the confidence interval from the output to write a statement about the set of plausible values for the parameter estimate, and to evaluate the plausibility of the null hypothesis.

h.) Use the null hypothesis to write a statement interpreting the p-value from the output. (Do not use more or less than 0.05.as reasoning)

Answer 1

a)
Sampling unit is flood affected areas of New Orleans.
Sample size is 46

b)
The associated variables are lead concentrations of blood of children before and after the flood. (lead$bloodLeadAfter and lead$bloodLeadBefore)
The scale of measurement is ug/dl

c)
As, there are two samples and same individuals (children) participated in the study before and after the floods,
this is a paired t-test

d) This may not be an appropriate design. More random samples of children from a particular area should be taken, to get the true population mean of lead concentrations of blood in the area.

e)
The the population parameter of interest is mean difference between lead concentrations of blood (in ug/dl) of children before (lead$bloodLeadBefore) and after the flood (lead$bloodLeadAfter).

f)

Null hypothesis H0: lead$bloodLeadAfter - lead$bloodLeadBefore = 0

g)

The plausible values for the parameter estimate lies in the range (-2.411851, -1.444671)

As, the confidence interval does not contain the value 0, we reject the null hypothesis.

h)

If null hypothesis is true, the probability of obtaining a significant mean difference is 3.107e-10 because of random sample error.