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 = -6.0538, df = 70.325, p-value = 6.212e-08

alternative hypothesis: true difference in means is not equal to 0

95% confidence interval: -2.563481 -1.293041

sample estimates: mean of x = 3.21087, mean of y = 5.13913

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

Sample size= df+1= 70.325+1=71.325=72

I think that you used the wrong test statistic for the test because the df is not a positive natural number. The required test statistic is paired t-test.

b) The variables are lead concentrations of blood and flood (before and after) The associated scales are the ratio (lead concentrations of blood) and nominal (flood).

c) The design name is paired t-test.

d) This is an appropriate design because that the lead concentrations of blood are measured before and after the flood for every individual. Hence, before and after the flood has a dependence.

e) the population parameter of interest is the population mean for the lead concentrations of blood for the difference between the before and after the flood.

f) Null Hypothesis: \mu=0

Alternative hypothesis: \mu>0

where difference =After-before.

g) The 95% confidence interval does not include that value zero> Hence, lead concentration is increased after the flood.

h) The p-value = 6.212e-08. Hence, reject the null hypothesis and conclude that lead concentration is increased after the flood at 0.05 level of significance.