Question

Iron-deficiency anemia is an important nutritional health problem in the Unites States. A dietary assessment was performed on 51 boys 9-11 years old whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.5 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among 9-11 years old boys from all income strata is known to be 14.44 mg. Researchers are wondering if the mean iron intake among the low-income group is different from that of the general population.

a) Based on the sample of 51 boys provide a 95% confidence interval for the mean daily iron intake among boys 9-11 years old whose families were below poverty level. Interpret the interval.

b) Perform an appropriate two-sided test at α = 0.05 to answer the researcher’s question. Interpret the results.

c) Are the results in a) and b) consistent?

Answer 1

a)

as 95% CI ; does not contain 14.44 as plausible value for population proportion ; therefore we can conclude mean iron intake among the low-income group is different from that of the general population

b)

as test statistic is in crtiical region we reject null hypothesis and conclude mean iron intake among the low-income group is different from that of the general population

c)

both the result from a and b are consistent