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) The individual lead concentrations of blood (in ug/dl) of children who lived in 46 different affected areas both before and after the floods is the sampling unit.

The sample size is df+1=45+1=46.

b) The interesting variable is lead concentrations of blood and its associated scale is the ratio.

c) The design name is paired t-test.

d) d.) This is an appropriate design because information is collected from the same individuals with two time that is before and after the floods. Hence, the two information are dependent.

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

f) The corresponding p-value = 3.107e-10 for the test is smaller than 0.05 level of significance. Hence, we can conclude that there is a significant increment in lead concentrations of blood (in ug/dl) of children after the floods at 0.05 level of significance.

g) The 95% CI does not include the value zero. Hence, reject the null hypothesis and conclude same with f).

h) same with h)