Hypothesis testing

1 Iron-deficiency anemia is an important nutritional health problem in the United 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 12.50 mg with standard deviation 4.75 mg. Suppose the mean daily iron intake among a large population of 9~11 years old boys from all income strata is 14.44 mg and the distribution is normal. We want to test if the mean iron intake among the low-income group is different from that of the general population.

1. State the hypothesis that we can use to consider this question.
2. Carry out the hypothesis test in 1 using the critical-value method with a α level of 0.05, and summarize your findings.
3. What is the p-value for the test conducted in 2?

(4) Compute a 95% CI for the underlying variance of daily iron intake in the low-income group. What can you infer from this confidence interval?

2.

Body weight [gm] inoculated [I] and uninoculated [U] plants

1. Provide a 95% confidence interval the mean pod weight in each group.
2. Suppose there is some overlap between the 95% confidence interval in problem 2a. Does this necessarily imply there is no significant difference between the mean pod weights for the 2 groups? Why or why not?
3. What test can be used to compare the mean pod weight between the two groups?
4. Perform the test in problem 2c, and report in p-value [2 – tail].
5. Provide a 95% confidence interval for the difference in mean pod weight between the two groups.

1. The goal of the Swiss Analgesic Study was to assess the effect of taking phenacetin-containing analgesics on kidney function and other health parameters. A group of 624 women were identified from workplaces near Basel, Switzerland, with high intake of phenacetin-containing analgesics. The level of NAPAP [N – acetyl P– aminophenyl] in urine was used as a marker of phenacetin intake. This constitutes the "study" group. In addition, the control group was 626 women were identified, from the same workplaces with normal in NAPAP levels, who were presumed to have low or no phenacetin intake. The study group was then subdivided into a high –NAPAP and a low –NAPAP subgroup of according to the absolute NAPAP level. However, both subgroups at higher NAPAP levels than the control group. The women were examined at baseline during 1967/1968 and also in 1969, 1970, 1971, 1972, 1975, and in 1978 and had their kidney function evaluated by several objective laboratory tests. Data set SWISS.DAT contains along longitudinal data on serum creatinine levels [an important index of kidney function] women in both the study group and the control group. Documentation for this data set is given in SWISS.DOC.
   1. One hypothesis is that analgesics abusers would have different serum creatinine profiles at baseline. Using the data from the baseline visit, can you address this question?
   2. A major hypothesis of the study is that women with higher phenacetin intake would show a greater change in serum creatinine compared to women with low phenacetin intake. Can you assess this issue using the longitudinal data in the data set? [hint: a simple approach for accomplishing this is a look at the change in serum creatinine between the baseline visit and the last follow-up visit].

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