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BIO STATIC HOMEWORK

1.      The forthcomingcited are substantiality magnitude refutation (BMI) scores appraised in 12 patients who are unconditional of diabetes and participating in a consider of promote factors for corpulence.  Substantiality magnitude refutation is appraised as the harmony of impressiveness in kilograms to altitude in meters squared.  Breed a 95% trust interim consider of the gentleman BMI.

 

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

 

 

2.      Consider the facts in Problem 1.  How multifarious subjects would be needed to fix that a 95% trust interim consider of BMI had a boundary of fault not comprehensive 2 units?

 

 

3.      The medium BMI in patients unconditional of diabetes was reverberationed as 28.2.  The investigator conducting the consider pictorial in Problem 1 hypothesizes that the BMI in patients unconditional of diabetes is preferable.  Based on the facts in Problem 1 is there declaration that the BMI is speakingly preferable that 28.2?  Use a 5% raze of sagacity. 

 

 

4.      Peak expiratory progress (PEF) is a appraise of a patient’s ability to evert air from the lungs.  Patients forthcoming a while asthma or other respiratory provisions repeatedly keep scientific PEF.  The medium PEF for fruit unconditional of asthma is 306.  An investigator shortnesss to endeavor whether fruit forthcoming a while constant bronchitis keep scientific PEF.  A pattern of 40 fruit forthcoming a while constant bronchitis are premeditated and their medium PEF is 279 forthcoming a while a government inconsequence of 71.  Is there statistical declaration of a inferior medium PEF in fruit forthcoming a while constant bronchitis?  Run the divert endeavor at a=0.05. 

 

 

5.      Consider intermittently the consider in Problem 4, a incongruous investigator conducts a remedy consider to summon whether there is a contrariety in medium PEF in fruit forthcoming a while constant bronchitis as paralleld to those forthcoming a whileout.  Facts on PEF are self-possessed and summarized underneath.  Based on the facts, is there statistical declaration of a inferior medium PEF in fruit forthcoming a while constant bronchitis as paralleld to those forthcoming a whileout?  Run the divert endeavor at a=0.05. 

 

Group

Number of Children

Mean PEF

Std Dev PEF

Chronic Bronchitis

25

281

68

No Constant Bronchitis

25

319

74

 

 

6.      Using the facts presented in Problem 5,

 

a)      Construct a 95% trust interim for the medium PEF in fruit forthcoming a whileout constant bronchitis.

b)      How multifarious fruit would be required to fix that the boundary of fault in (a) does not excel 10 units?

 

 

7.      A clinical endeavor is run to summon the agency of an tentative garbage in reducing preterm gift to a garbage considered government heed and to placebo.  Indicative women are enrolled and randomly assigned to entertain either the tentative garbage, the government garbage or placebo.  Women are flourished through gift and classified as concedeing preterm (< 37 weeks) or not.  The facts are appearancen underneath.

 

Preterm Delivery

Experimental Drug

Standard Drug

Placebo

Yes

17

23

35

No

83

77

65

 

Is there a statistically speaking contrariety in the distributions of women concedeing preterm discurrent the three composition classs?  Run the endeavor at a 5% raze of sagacity.

 

 

8.      Using the facts in Problem 7, breed a 95% trust interim for the contrariety in distributions of women concedeing preterm in the tentative and government garbage composition classs. 

 

 

9.      Consider the facts presented in Problem 7.  Previous studies keep appearancen that almost 32% of women concede prematurely forthcoming a whileout composition.  Is the distribution of women concedeing prematurely speakingly preferable in the placebo class?  Run the endeavor at a 5% raze of sagacity. 

 

 

10.  A consider is run comparing HDL cholesterol razes betwixt men who luxuriance constantly and those who do not.  The facts are appearancen underneath.

 

Regular Exercise

N

Mean

Std Dev

Yes

35

48.5

12.5

No

120

56.9

11.9

 

Generate a 95% trust interim for the contrariety in medium HDL razes betwixt men who luxuriance constantly and those who do not. 

 

 

11.  A clinical endeavor is run to assess the goods of incongruous contrives of recurrent luxuriance on HDL razes in individuals betwixt the ages of 18 and 29.  Participants in the consider are randomly assigned to one of three luxuriance classs - Impressiveness luxuriance, Aerobic luxuriance or Stretching/Yoga – and instructed to flourish the program for 8 weeks.  Their HDL razes are appraised forthcoming 8 weeks and are summarized underneath.

 

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 speaking contrariety in medium HDL razes discurrent the luxuriance classs?  Run the endeavor at a 5% raze of sagacity.  HINT:  SSfault =  7286.5. 

 

 

12.  Consider intermittently the facts in Problem 11.  Imagine that in the aerobic luxuriance class we to-boot appraised the sum of hours of aerobic luxuriance per week and the medium is 5.2 hours forthcoming a while a government inconsequence of 2.1 hours.  The pattern apposition is -0.42. 

 

a)      Estimate the equation of the retrogression sequence that best describes the intercommunity betwixt sum of hours of luxuriance per week and HDL cholesterol raze (Assume that the relying shifconsultation is HDL raze). 

b)      Estimate the HDL raze for a peculiar who luxuriances 7 hours per week.

c)      Estimate the HDL raze for a peculiar who does not luxuriance.

 

 

13.  The board underneathneath summarizes basesequence characteristics on patients participating in a clinical endeavor.

 

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) Whole Cholesterol

214 + 24.9

210 + 23.1

0.8954

% Current Smokers

17%

15%

0.5741

% forthcoming a while Diabetes

8%

3%

0.0438

 

a)      Are there any statistically speaking contrarietys in basesequence characteristics betwixt composition classs?  Justify your solution.

b)      Write the hypotheses and the endeavor statistic used to parallel ages betwixt classs.  (No calculations – natural H0, H1 and contrive of the endeavor statistic)

c)      Write the hypotheses and the endeavor statistic used to parallel % females betwixt classs.  (No calculations – natural H0, H1 and contrive of the endeavor statistic)

d)     Write the hypotheses and the endeavor statistic used to parallel educational razes betwixt classs.  (No calculations – natural H0, H1 and contrive of the endeavor statistic)

 

 

14.  A consider is purposed to summon whether there is a contrariety in confutation to incongruous compositions in patients forthcoming a while rheumatoid arthritis.  The fruit is patient’s self-reported result of composition.  The facts are appearancen underneath.  Is there a speaking contrariety in result of composition?  Run the endeavor at a 5% raze of sagacity. 

 

 

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 facts appearancen in Problem 14, imagine we nucleus on the distributions of patients who appearance acception.  Is there a statistically speaking contrariety in the distributions of patients who appearance acception betwixt compositions 1 and 2.  Run the endeavor at a 5% raze of sagacity. 

 

 

16.  An partition is conducted to parallel medium space-among to affliction exemption (measured in minutes) underneathneath filthy competing composition regimens Summary statistics on the filthy compositions are appearancen underneath.

 

Treatment

Sample Size

Mean Space-among 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 forthcomingcited ANOVA Table

 

 

 

 

 

Source of Variation

SS

df

MS

F

Between Groups

 

 

 

 

Within Groups

3719.48

 

 

 

 

 

 

 

 

Total

 

 

 

 

 

b)   Write the hypotheses to be endeavored.

c)   Write the determination government.

d)   What is the omission?

 

 

 

17.  The forthcomingcited facts were self-possessed in a clinical endeavor to parallel a new garbage to a placebo for its agency in inferioring whole serum cholesterol.  Breed a 95% trust interim for the contrariety in medium whole cholesterol razes betwixt compositions.

 

 

New Drug

(n=75)

Placebo

(n=75)

Total Sample

(n=150)

Mean (SD) Whole Serum Cholesterol

185.0 (24.5)

204.3 (21.8)

194.7 (23.2)

% Patients forthcoming a while Whole Cholesterol < 200

78.0%

65.0%

71.5%

 

 

18.  Using the facts in Problem 17,

 

a)      Generate a 95% trust interim for the distribution of all patients forthcoming a while whole cholesterol < 200. 

b)      How multifarious patients would be required to fix that a 95% trust interim has a boundary of fault not comprehensive 5%? 

 

 

19.  A minute guide consider is conducted to summon the result of a nutritional appendix on whole substantiality impressiveness.  Six participants accord to accept the nutritional appendix.  To assess its result on substantiality impressiveness, impressivenesss are appraised anteriorly starting the appendixation and then forthcoming 6 weeks.  The facts are appearancen underneath.  Is there a speaking acception in substantiality impressiveness forthcomingcited appendixation?  Run the endeavor at a 5% raze of sagacity. 

 

Subject

Initial Weight

Weight forthcoming 6 Weeks

1

155

157

2

142

145

3

176

180

4

180

175

5

210

209

6

125

126

 

 

20.  The forthcomingcited board was presented in an season summarizing a consider to parallel a new garbage to a government garbage 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

% forthcoming a while Insurance

87%

65%

82%

0.0352

Disease Stage

 

 

 

0.0261

  Position I

35%

18%

33%

 

  Position II

42%

37%

47%

 

  Position III

23%

51%

20%

 

*Table entries and Medium (SD) or %

 

a)      Are there any statistically speaking contrarietys in the characteristics appearancen discurrent the compositions?   Justify your solution.

b)      Consider the endeavor for contrarietys in age discurrent compositions.  Write the hypotheses and the contriveula of the endeavor statistic used (No computations required – contriveula barely).

c)      Consider the endeavor for contrarietys in insurance coverage discurrent compositions.  Write the hypotheses and the contriveula of the endeavor statistic used (No computations required – contriveula barely).

d)     Consider the endeavor for contrarietys in complaint position discurrent compositions.  Write the hypotheses and the contriveula of the endeavor statistic used (No computations required – contriveula barely).

 

 

21.  A minute guide consider is run to parallel a new garbage for constant affliction to one that is currently conducive.  Participants are randomly assigned to entertain either the new garbage or the currently conducive garbage and reverberation acception in affliction on a 5-object ordinal scale: 1=Pain is considerable worse, 2=Pain is partially worse, 3= No shift, 4=Pain improved partially, 5=Pain considerable improved.  Is there a speaking contrariety in self-reported acception in affliction?  Use the Mann-Whitney U endeavor forthcoming a while a 5% raze of sagacity.

 

New Drug:                        4          5          3          3          4          2

Standard Drug:     2          3          4          1          2          3

 

 

22.  Answer Gentleman or Fib to each of the forthcomingcited

a)      The boundary of fault is frequently main than or correspondent to the government fault.

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

c)      If a 95% CI for the contrariety in two inrelying mediums is (-4.5 to 2.1), then the object consider is -2.1.

d)     If a 95% CI for the contrariety in two inrelying mediums is (2.1 to 4.5), there is no speaking contrariety in mediums.

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

 

 

23.  A randomized inferior endeavor is run to evaluate the agency of a new garbage for asthma in fruit. A whole of 250 fruit are randomized to either the new garbage or placebo (125 per class).  The medium age of fruit assigned to the new garbage is 12.4 forthcoming a while a government inconsequence of 3.6 years.  The medium age of fruit assigned to the placebo is 13.0 forthcoming a while a government inconsequence of 4.0 years.  Is there a statistically speaking contrariety in ages of fruit assigned to the compositions?  Run the divert endeavor at a 5% raze of sagacity.

 

 

24.  Consider intermittently the randomized inferior endeavor pictorial in Problem 22.  Imagine that there are 63 boys assigned to the new garbage class and 58 boys assigned to the placebo.  Is there a statistically speaking contrariety in the distributions of boys assigned to the compositions?  Run the divert endeavor at a 5% raze of sagacity.

 

 

25.  A clinical endeavor is run to evaluate the agency of a new garbage to bar preterm gift.  A whole of n=250 indicative women accord to have-a-share and are randomly assigned to entertain either the new garbage or a placebo and flourished through the progress of pregnancy.   Discurrent 125 women receiving the new garbage, 24 concede preterm and discurrent 125 women receiving the placebo, 38 concede preterm.  Construct a 95% trust interim for the contrariety in distributions of women who concede preterm. 

 

 

26.  “Average adult Americans are about one inch taller, but closely a whopping 25 pounds heavier than they were in 1960, according to a new reverberation from the Centers for Complaint Control and Prevention (CDC). The bad tidings, says CDC is that mediocre BMI (substantiality magnitude refutation, a impressiveness-for-altitude contriveula used to appraise corpulence) has acceptiond discurrent adults from almost 25 in 1960 to 28 in 2002.”   Boston is considered one of America’s healthiest cities – is the impressiveness find gone 1960 harmonious in Boston?  A pattern of n=25 adults suggested a medium acception of 17 pounds forthcoming a while a government inconsequence of 8.6 pounds.  Is Boston statistically speakingly incongruous in stipulations of impressiveness find gone 1960?  Run the divert endeavor at a 5% raze of sagacity.

 

 

27.   In 2007, the CDC reverberationed that almost 6.6 per 1000 (0.66%) fruit were forced forthcoming a while autism spectrum guess-work.   A pattern of 900 fruit from Boston are endeavored and 7 are diagnosed forthcoming a while autism spectrum guess-work.  Is the distribution of fruit forced forthcoming a while autism spectrum guess-work preferable in Boston as paralleld to the open consider?  Run the divert endeavor at a 5% raze of sagacity. 

 

 

28.  A clinical endeavor is life intentional to summon the result of a new tentative garbage purposed to impoverish whole serum cholesterol.  Investigators succeed enroll participants forthcoming a while whole cholesterol razes betwixt 200-240, they succeed be randomized to entertain the new garbage or a placebo and flourished for 2 months, and the whole cholesterol succeed be appraised.  Investigators guile to run a endeavor of fancy and shortness 80% dominion to expose a contrariety of 10 objects in medium whole cholesterol razes betwixt classs.  They mismisappropriate that 10% of the participants randomized succeed be past balance the 2 month flourish-up.  How multifarious participants must be enrolled in the consider?  Misappropriate that the government inconsequence of whole cholesterol is 18.5.

 

 

29.  An observational consider is conducted to summon the alliance betwixt age and whole serum cholesterol.  The apposition is considerd at r = 0.35.  The consider involves n=125 participants and the medium (std dev) age is 44.3 (10.0) years forthcoming a while an age collocate of 35 to 55 years, and medium (std dev) whole cholesterol is 202.8 (38.4).

 

a)     Estimate the equation of the sequence that best describes the alliance betwixt age (as the inrelying shiftable) and whole serum cholesterol.

b)     Estimate the whole serum cholesterol for a 50-year old peculiar. 

c)      Estimate the whole serum cholesterol for a 70-year old peculiar. 

 

 

30.  For each proposition underneath, evidence whether the proposition is gentleman or fib.

 

a)      In logistic retrogression, the predictors are dichotomous, and the fruit is a faithful shiftable.

b)      When careful a apposition coefficient betwixt two faithful shiftables, the scales on which the shiftables are appraised move the appreciate of the apposition coefficient.

c)      It is aggravate unamenable to repudiate a ineffectual fancy if we use a 10% raze of sagacity paralleld forthcoming a while a 5% raze of sagacity.  

d)     The pattern greatness required to expose an result greatness of 0.25 is larger than the pattern greatness required to expose an result greatness of 0.50 forthcoming a while 80% dominion and a 5% raze of sagacity.  

 

 

31.  For each topic underneath, afford a mean (1-2 sentences) confutation.

 

a)      How is the tower coefficient (b1) in a single-minded sequencear retrogression incongruous than the coefficient (b1) in a multiple sequencear retrogression standard?

b)      When would a fife partition standard be used instead of a logistic retrogression standard?

c)      What is the divert statistical endeavor to assess whether there is an alliance betwixt corpulence foundation (natural impressiveness, balanceweight, brawny) and 5-year bright cardiovascular complaint (CVD)?  Imagine each participant’s corpulence foundation (category) is notorious as is whether they eliminate CVD balance the present 5 years or not.

 

 

32.  An observational consider is conducted to parallel experiences of men and women betwixt the ages of 50-59 years forthcomingcited coronary artery bypass surgery.  Participants underneathgo the surgery and are flourished until the space-among of termination, until they are past to flourish-up or up to 30 years, whichever comes primitive.  The forthcomingcited board details the experiences of participating men and women.  The facts underneathneath are years of termination or years of decisive touch for men and women.

 

 

Men

 

Women

Year of Death

Year of Decisive Contact

 

Year of Death

Year of Decisive 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 Consider the fife functions for each composition class using the Kaplan-Meier approach

b)      Test if there is a speaking contrariety in fife betwixt composition classs using the log collocate endeavor and a 5% raze of sagacity.