Question

Iron-deficiency anemia is an important nutritional health problem in the United States. A dietary as- sessment was performed on 51 boys 9 to 11 years of age whose families were below the poverty level. The mean daily iron intake among these boys was found to be 12.50mg with standard deviation 4.75mg. Suppose the mean daily iron intake among a large population of 9 to 11 year-old boys from all income strata is 14.44 mg. We want to test whether the mean iron intake among the low-income group is different from that of the general population. 1. State the hypotheses that we can use to consider this question. 2. Carry out the hypothesis test using the critical-value method with an a level of 0.05, and summarize your findings. 3. What is the p-value for the test? The standard deviation of daily iron intake in the larger population of 9 to 11 year-old boys was 5.56 ng We want to test whether the standard deviation from the low-income group is comparable to that of the general population. 1. State the hypotheses that we can use to answer this question. 2. Carry out the test using the critical value method with an a level of 0.05, and summarize your findings. 3. What is the p-value for the test? 4. Compute a 95% CI for the underlying variance of daily iron intake in the low-income group, what can you infer from this CI?

Answer 1

1.

Ho: μ=14.44

Ha: μ =/= 14.44

2. & 3.

Z= (Xbar-μ)/(sd/sqrt(n))

=(12.50-14.44) / (4.75 / sqrt(51))

=-2.91671

Critical Z_ck values for 95% conf interval is -/+ 1.96

Since Z calculated doesn't fall under Z_ck 's range of -/+ 1.96 we can conclude that we have to reject Ho

Hence we can say that the mean i/c of low i/c group is different from population

Looking from the Z table and find the p value we get area under the curve as 0.001768723

Since this is a two tail test the p value = 2*0.001768723=0.003537445

As per the HOMEWORKLIB POLICY we are supposed to answer 1st question only still I have gone ahead and answered 3. If you want the ans for the rest pls. post it separately. Hope you understand.

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!