DescriptionMSC 600 Quantitative Methods
1) The National Health Statistics Reports dated Oct. 22, 2008, included the following information
on the heights (in.) for non-Hispanic white females:
Std. Error Mean
60 and older
a) Calculate and interpret a confidence interval at confidence level approximately 95% for the
difference between population mean height for the younger women and that for the older
b) Let 1 denote the population mean height for those aged 20-39 and 2 denote the
population mean height for those aged 60 and older. Interpret the hypotheses 0 : 1 −
2 = 1 and : 1 − 2 > 1, and then carry out a test of these hypotheses at significance
level .001 using the rejection region approach.
c) What is the P-value for the test you carried out in (b)? Based on this P-value, would you
reject the null hypothesis at any reasonable significance level? Explain.
d) What hypotheses would be appropriate if 1 referred to the older age group, 2 referred to
the younger age group, and you wanted to see if there was compelling evidence for
concluding that the population mean height for younger women exceeded that for older
women by more than 1 in.?
2) The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as
knee. The article “Evidence of Mechanical Load Redistribution at the Knee Joint in the Elderly
when Ascending Stairs and Ramps” (Annals of Biomed. Engr., 2008:467-476) presented the
following summary data on stance duration (ms) for samples of both older and younger adults.
Assume that both stance duration distributions are normal. Carry out a test of hypotheses at
significance level .05 to decide whether true average stance duration is larger among elderly
individuals than among younger individuals. (Population variances are not assumed equal.)
3) Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for
milk production. The paper “Bone Mass Is Recovered from Lactation to Postweaning in
Adolescent Mothers with Low Calcium Intakes” (Amer. J. of Clinical Nutr., 2004:1322-1326) gave
the following data on total body bone mineral content (TBBMC) (g) for a sample both during
lactation (L) and in postweaning period (P). (Let = true mean difference in TBBMC,
postweaning minus lactation.)
MSC 600 Quantitative Methods
a) Does the data suggest that true average total body bone mineral content during
postweaning exceeds that during lactation by more than 25 g? State and test the
appropriate hypotheses using a significance level of .05. [Note: The appropriate normal
probability plot shows some curvature but not enough to cast substantial doubt on a
b) Does the (incorrect) use of the two-sample t test to test the hypotheses suggested in (a)
lead to the same conclusion that you obtained here? Explain.
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