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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