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BIO STATIC HOMEWORK

1.      The subjoined are collection bulk condemnation (BMI) scores prized in 12 patients who are bounteous of diabetes and participating in a con-balance of risk factors for corpulence.  Collection bulk condemnation is prized as the accordment of gravity in kilograms to elevation in meters squared.  Originate a 95% dependence intermission prize of the penny BMI.

25           27        31        33        26        28        38        41        24        32        35        40

2.      Consider the grounds in Problem 1.  How abundant subjects would be needed to determine that a 95% dependence intermission prize of BMI had a edge of untruth not large 2 units?

3.      The balance BMI in patients bounteous of diabetes was tidingsed as 28.2.  The investigator conducting the con-balance pictorial in Problem 1 hypothesizes that the BMI in patients bounteous of diabetes is better.  Based on the grounds in Problem 1 is there experimentimony that the BMI is momentously better that 28.2?  Use a 5% smooth of view.

4.      Peak expiratory progress (PEF) is a prize of a patient’s dominion to emit air from the lungs.  Patients behind a while asthma or other respiratory stipulations repeatedly entertain detested PEF.  The balance PEF for eliminatement bounteous of asthma is 306.  An investigator lacks to experiment whether eliminatement behind a while consecutive bronchitis entertain detested PEF.  A case of 40 eliminatement behind a while consecutive bronchitis are premeditated and their balance PEF is 279 behind a while a appraise irregularity of 71.  Is there statistical experimentimony of a inferior balance PEF in eliminatement behind a while consecutive bronchitis?  Run the behind a whilehold experiment at a=0.05.

5.      Consider repeatedly the con-balance in Problem 4, a contrariant investigator conducts a assist con-balance to summon whether there is a disagreement in balance PEF in eliminatement behind a while consecutive bronchitis as collated to those behind a whileout.  Grounds on PEF are serene and summarized beneath.  Based on the grounds, is there statistical experimentimony of a inferior balance PEF in eliminatement behind a while consecutive bronchitis as collated to those behind a whileout?  Run the behind a whilehold experiment at a=0.05.

Group

Number of Children

Mean PEF

Std Dev PEF

Chronic Bronchitis

25

281

68

No Consecutive Bronchitis

25

319

74

6.      Using the grounds presented in Problem 5,

a)      Construct a 95% dependence intermission for the balance PEF in eliminatement behind a whileout consecutive bronchitis.

b)      How abundant eliminatement would be required to determine that the edge of untruth in (a) does not surpass 10 units?

7.      A clinical grief is run to summon the competency of an tentative refuse in reducing preterm endowment to a refuse considered appraise concern and to placebo.  Generative women are embodyed and randomly assigned to admit either the tentative refuse, the appraise refuse or placebo.  Women are thriveed through endowment and classified as set freeing preterm (< 37 weeks) or not.  The grounds are likenessn beneath.

Preterm Delivery

Experimental Drug

Standard Drug

Placebo

Yes

17

23

35

No

83

77

65

Is there a statistically momentous disagreement in the interrelationships of women set freeing preterm incomplete the three matter orders?  Run the experiment at a 5% smooth of view.

8.      Using the grounds in Problem 7, originate a 95% dependence intermission for the disagreement in interrelationships of women set freeing preterm in the tentative and appraise refuse matter orders.

9.      Consider the grounds presented in Problem 7.  Previous studies entertain likenessn that almost 32% of women set free prematurely behind a whileout matter.  Is the interconformity of women set freeing prematurely momentously better in the placebo order?  Run the experiment at a 5% smooth of view.

10.  A con-balance is run comparing HDL cholesterol smooths betwixt men who inoculation constantly and those who do not.  The grounds are likenessn beneath.

Regular Exercise

N

Mean

Std Dev

Yes

35

48.5

12.5

No

120

56.9

11.9

Generate a 95% dependence intermission for the disagreement in balance HDL smooths betwixt men who inoculation constantly and those who do not.

11.  A clinical grief is run to assess the proceeds of contrariant frames of frameal inoculation on HDL smooths in people betwixt the ages of 18 and 29.  Participants in the con-balance are randomly assigned to one of three inoculation orders - Gravity inoculation, Aerobic inoculation or Stretching/Yoga – and instructed to thrive the program for 8 weeks.  Their HDL smooths are prized behind 8 weeks and are summarized beneath.

Exercise Group

N

Mean

Std Dev

Weight Training

20

49.7

10.2

Aerobic Exercise

20

43.1

11.1

Stretching/Yoga

20

57.0

12.5

Is there a momentous disagreement in balance HDL smooths incomplete the inoculation orders?  Run the experiment at a 5% smooth of view.  HINT:  SSuntruth =  7286.5.

12.  Consider repeatedly the grounds in Problem 11.  Deem that in the aerobic inoculation order we to-boot prized the sum of hours of aerobic inoculation per week and the balance is 5.2 hours behind a while a appraise irregularity of 2.1 hours.  The case mutuality is -0.42.

a)      Estimate the equation of the retreat outoutsuccession that best describes the conformity betwixt sum of hours of inoculation per week and HDL cholesterol smooth (Assume that the resting capricious is HDL smooth).

b)      Estimate the HDL smooth for a idiosyncratic who inoculations 7 hours per week.

c)      Estimate the HDL smooth for a idiosyncratic who does not inoculation.

13.  The board beneath summarizes baseoutsuccession characteristics on patients participating in a clinical grief.

Characteristic

Placebo (n=125)

Experimental (n=125)

P

Mean (+ SD) Age

54 + 4.5

53 + 4.9

0.7856

% Female

39%

52%

0.0289

% Less than High School Education

24%

22%

0.0986

% Completing High School

37%

36%

% Completing Some College

39%

42%

Mean (+ SD) Systolic Blood Pressure

136 + 13.8

134 + 12.4

0.4736

Mean (+ SD) Completion Cholesterol

214 + 24.9

210 + 23.1

0.8954

% Current Smokers

17%

15%

0.5741

% behind a while Diabetes

8%

3%

0.0438

a)      Are there any statistically momentous disagreements in baseoutsuccession characteristics betwixt matter orders?  Justify your counter-argument.

b)      Write the hypotheses and the experiment statistic used to collate ages betwixt orders.  (No calculations – honest H0, H1 and frame of the experiment statistic)

c)      Write the hypotheses and the experiment statistic used to collate % females betwixt orders.  (No calculations – honest H0, H1 and frame of the experiment statistic)

d)     Write the hypotheses and the experiment statistic used to collate educational smooths betwixt orders.  (No calculations – honest H0, H1 and frame of the experiment statistic)

14.  A con-balance is purposed to summon whether there is a disagreement in reply to sundry matters in patients behind a while rheumatoid arthritis.  The eliminatement is patient’s self-reported goods of matter.  The grounds are likenessn beneath.  Is there a momentous disagreement in goods of matter?  Run the experiment at a 5% smooth of view.

Symptoms

Worsened

No Effect

Symptoms Improved

Total

Treatment 1

22

14

14

50

Treatment 2

14

15

21

50

Treatment 3

9

12

29

50

15.  Using the grounds likenessn in Problem 14, deem we rendezvous on the interrelationships of patients who likeness advancement.  Is there a statistically momentous disagreement in the interrelationships of patients who likeness advancement betwixt matters 1 and 2.  Run the experiment at a 5% smooth of view.

16.  An partition is conducted to collate balance period to asceticism assistance (measured in minutes) underneathneath four competing matter regimens Summary statistics on the four matters are likenessn beneath.

Treatment

Sample Size

Mean Period to Relief

Sample Variance

A

5

33.8

17.7

B

5

27.0

15.5

C

5

50.8

9.7

D

5

39.6

16.8

a)      Complete the subjoined ANOVA Table

Source of Variation

SS

df

MS

F

Between Groups

Within Groups

3719.48

Total

b)   Write the hypotheses to be experimented.

c)   Write the sentence government.

d)   What is the falsification?

17.  The subjoined grounds were serene in a clinical grief to collate a new refuse to a placebo for its competency in inferioring completion serum cholesterol.  Originate a 95% dependence intermission for the disagreement in balance completion cholesterol smooths betwixt matters.

New Drug

(n=75)

Placebo

(n=75)

Total Sample

(n=150)

Mean (SD) Completion Serum Cholesterol

185.0 (24.5)

204.3 (21.8)

194.7 (23.2)

% Patients behind a while Completion Cholesterol < 200

78.0%

65.0%

71.5%

18.  Using the grounds in Problem 17,

a)      Generate a 95% dependence intermission for the interconformity of all patients behind a while completion cholesterol < 200.

b)      How abundant patients would be required to determine that a 95% dependence intermission has a edge of untruth not large 5%?

19.  A little direct con-balance is conducted to summon the goods of a nutritional addition on completion collection gravity.  Six participants accord to transfer the nutritional addition.  To assess its goods on collection gravity, gravitys are prized antecedently starting the additionation and then behind 6 weeks.  The grounds are likenessn beneath.  Is there a momentous growth in collection gravity subjoined additionation?  Run the experiment at a 5% smooth of view.

Subject

Initial Weight

Weight behind 6 Weeks

1

155

157

2

142

145

3

176

180

4

180

175

5

210

209

6

125

126

20.  The subjoined board was presented in an season summarizing a con-balance to collate a new refuse to a appraise refuse and to a placebo.

Characteristic*

New Drug

Standard Drug

Placebo

p

Age, years

45.2 (4.8)

44.9 (5.1)

42.8 (4.3)

0.5746

% Female

51%

55%

57%

0.1635

Annual Income, \$000s

59.5 (14.3)

63.8 (16.9)

58.2 (13.6)

0.4635

% behind a while Insurance

87%

65%

82%

0.0352

Disease Stage

0.0261

Class I

35%

18%

33%

Class II

42%

37%

47%

Class III

23%

51%

20%

*Table entries and Balance (SD) or %

a)      Are there any statistically momentous disagreements in the characteristics likenessn incomplete the matters?   Justify your counter-argument.

b)      Consider the experiment for disagreements in age incomplete matters.  Write the hypotheses and the frameula of the experiment statistic used (No computations required – frameula solely).

c)      Consider the experiment for disagreements in insurance coverage incomplete matters.  Write the hypotheses and the frameula of the experiment statistic used (No computations required – frameula solely).

d)     Consider the experiment for disagreements in complaint class incomplete matters.  Write the hypotheses and the frameula of the experiment statistic used (No computations required – frameula solely).

21.  A little direct con-balance is run to collate a new refuse for consecutive asceticism to one that is currently profitable.  Participants are randomly assigned to admit either the new refuse or the currently proficonsideration refuse and tidings advancement in asceticism on a 5-apex ordinal scale: 1=Pain is greatly worse, 2=Pain is subordinately worse, 3= No modify, 4=Pain improved subordinately, 5=Pain greatly improved.  Is there a momentous disagreement in self-reported advancement in asceticism?  Use the Mann-Whitney U experiment behind a while a 5% smooth of view.

New Drug:                        4          5          3          3          4          2

Standard Drug:     2          3          4          1          2          3

22.  Answer Penny or Mendacious to each of the subjoined

a)      The edge of untruth is constantly important than or resembling to the appraise untruth.

b)      If a experiment is run and p=0.0356, then we can discard H0 at a=0.01.

c)      If a 95% CI for the disagreement in two inresting balances is (-4.5 to 2.1), then the apex prize is -2.1.

d)     If a 95% CI for the disagreement in two inresting balances is (2.1 to 4.5), there is no momentous disagreement in balances.

e)      If a 90% CI for the balance is (75.3 to 80.9), we would discard H0: m=70 in boon of H1: m≠70 at a=0.05.

23.  A randomized controlled grief is run to evaluate the competency of a new refuse for asthma in eliminatement. A completion of 250 eliminatement are randomized to either the new refuse or placebo (125 per order).  The balance age of eliminatement assigned to the new refuse is 12.4 behind a while a appraise irregularity of 3.6 years.  The balance age of eliminatement assigned to the placebo is 13.0 behind a while a appraise irregularity of 4.0 years.  Is there a statistically momentous disagreement in ages of eliminatement assigned to the matters?  Run the behind a whilehold experiment at a 5% smooth of view.

24.  Consider repeatedly the randomized controlled grief pictorial in Problem 22.  Deem that there are 63 boys assigned to the new refuse order and 58 boys assigned to the placebo.  Is there a statistically momentous disagreement in the interrelationships of boys assigned to the matters?  Run the behind a whilehold experiment at a 5% smooth of view.

25.  A clinical grief is run to evaluate the competency of a new refuse to nullify preterm endowment.  A completion of n=250 generative women accord to have-a-share and are randomly assigned to admit either the new refuse or a placebo and thriveed through the sequence of pregnancy.   Incomplete 125 women receiving the new refuse, 24 set free preterm and incomplete 125 women receiving the placebo, 38 set free preterm.  Construct a 95% dependence intermission for the disagreement in interrelationships of women who set free preterm.

26.  “Average adult Americans are environing one inch taller, but closely a whopping 25 pounds heavier than they were in 1960, according to a new tidings from the Centers for Complaint Control and Prevention (CDC). The bad information, says CDC is that medium BMI (collection bulk condemnation, a gravity-for-elevation frameula used to prize corpulence) has growthd incomplete adults from almost 25 in 1960 to 28 in 2002.”   Boston is considered one of America’s healthiest cities – is the gravity compel since 1960 congruous in Boston?  A case of n=25 adults suggested a balance growth of 17 pounds behind a while a appraise irregularity of 8.6 pounds.  Is Boston statistically momentously contrariant in provisions of gravity compel since 1960?  Run the behind a whilehold experiment at a 5% smooth of view.

27.   In 2007, the CDC tidingsed that almost 6.6 per 1000 (0.66%) eliminatement were abtypical behind a while autism spectrum assumption.   A case of 900 eliminatement from Boston are experimented and 7 are diagnosed behind a while autism spectrum assumption.  Is the interconformity of eliminatement abtypical behind a while autism spectrum assumption better in Boston as collated to the open prize?  Run the behind a whilehold experiment at a 5% smooth of view.

28.  A clinical grief is nature calculated to summon the goods of a new tentative refuse purposed to diminish completion serum cholesterol.  Investigators obtain embody participants behind a while completion cholesterol smooths betwixt 200-240, they obtain be randomized to admit the new refuse or a placebo and thriveed for 2 months, and the completion cholesterol obtain be prized.  Investigators project to run a experiment of theory and lack 80% dominion to unmask a disagreement of 10 apexs in balance completion cholesterol smooths betwixt orders.  They feign that 10% of the participants randomized obtain be obsolete balance the 2 month thrive-up.  How abundant participants must be embodyed in the con-over?  Feign that the appraise irregularity of completion cholesterol is 18.5.

29.  An observational con-balance is conducted to summon the contortment betwixt age and completion serum cholesterol.  The mutuality is prized at r = 0.35.  The con-balance involves n=125 participants and the balance (std dev) age is 44.3 (10.0) years behind a while an age class of 35 to 55 years, and balance (std dev) completion cholesterol is 202.8 (38.4).

a)     Estimate the equation of the outoutsuccession that best describes the contortment betwixt age (as the inresting capricious) and completion serum cholesterol.

b)     Estimate the completion serum cholesterol for a 50-year old idiosyncratic.

c)      Estimate the completion serum cholesterol for a 70-year old idiosyncratic.

30.  For each assertion beneath, betray whether the assertion is penny or mendacious.

a)      In logistic retreat, the predictors are dichotomous, and the eliminatement is a consecutive capricious.

b)      When wary a mutuality coefficient betwixt two consecutive capriciouss, the scales on which the capriciouss are prized like the prize of the mutuality coefficient.

c)      It is aggravate perplexing to discard a null theory if we use a 10% smooth of view collated behind a while a 5% smooth of view.

d)     The case bigness required to unmask an goods bigness of 0.25 is larger than the case bigness required to unmask an goods bigness of 0.50 behind a while 80% dominion and a 5% smooth of view.

31.  For each investigation beneath, produce a brief (1-2 sentences) reply.

a)      How is the emerge coefficient (b1) in a artless outrectidirect retreat contrariant than the coefficient (b1) in a multiple outrectidirect retreat type?

b)      When would a planting partition type be used instead of a logistic retreat type?

c)      What is the behind a whilehold statistical experiment to assess whether there is an contortment betwixt corpulence foundation (typical gravity, balanceweight, oleaginous) and 5-year shining cardiovascular complaint (CVD)?  Deem each participant’s corpulence foundation (category) is unconcealed as is whether they eliminate CVD balance the next 5 years or not.

32.  An observational con-balance is conducted to collate experiences of men and women betwixt the ages of 50-59 years subjoined coronary artery bypass surgery.  Participants underneathgo the surgery and are thriveed until the period of expiration, until they are obsolete to thrive-up or up to 30 years, whichever comes principal.  The subjoined board details the experiences of participating men and women.  The grounds beneath are years of expiration or years of ultimate touch for men and women.

Men

Women

Year of Death

Year of Ultimate Contact

Year of Death

Year of Ultimate Contact

5

8

19

4

12

17

20

9

14

24

21

14

23

26

24

15

29

26

17

27

19

29

21

30

22

30

24

30

25

30

a)      Estimate the Prize the planting functions for each matter order using the Kaplan-Meier approach

b)      Test if there is a momentous disagreement in planting betwixt matter orders using the log arrange experiment and a 5% smooth of view.