DescriptionMSC 600 Quantitative Methods
HW2
1) The National Health Statistics Reports dated Oct. 22, 2008, included the following information
on the heights (in.) for non-Hispanic white females:
Age
Sample Size
Sample Mean
Std. Error Mean
20-39
866
64.9
.09
60 and older
934
63.1
.11
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
women.
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.
Age
Older
Younger
Sample Size
28
16
Sample Mean
801
780
Sample SD
117
72
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.)
Subject
1
2
3
4
5
6
7
8
9
10
L
1928
2549
2825
1924
1628
2175
2114
2621
1843
2541
P
2126
2885
2895
1942
1750
2184
2164
2626
2006
2627
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
normality assumption.]
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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