Harvard University Health Stats Worksheet

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FureelXvat

Mathematics

Harvard University

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Question 2

What is the crude mortality rate?

Age-Group

Population

Number of Deaths

<30

15,000

20

30-65

17,000

55

>65

6,000

155

a.

230

b.

6.1 per 1,000

c.

8.6 per 1,000

d.

6.1 per 10,000

Question 3

The age-specific death rate for the over-65 age group is

Age-Group

Population

Number of Deaths

<30

15,000

20

30-65

17,000

55

>65

6,000

155

a.

155

b.

25.8 per 1,000

c.

1.55 per 10,000

d.

25.8 per 10,000

Question 4

Calculate the relative risk of stroke of male smokers to male nonsmokers

Stroke

Smokers

Yes

No

Total

Yes

171

3,264

3,435

No

117

4,320

4,437

Total

288

7,584

7,872

a.

1.54

b.

1.88

c.

2.08

d.

None of the above is correct

Question 5

Calculate the odds ratio of having a stroke in men who smoke to those who do not smoke

Stroke

Smokers

Yes

No

Total

Yes

171

3,264

3,435

No

117

4,320

4,437

Total

288

7,584

7,872

a.

1.93

b.

1.88

c.

1.78

d.

1.34

Question 6

Is the following interpretation of the odds ratio true or false?
The odds of having a stoke are 1.93 times higher in men who smoke than in men who do not smoke

Stroke

Smokers

Yes

No

Total

Yes

171

3,264

3,435

No

117

4,320

4,437

Total

288

7,584

7,872

True

False

Question 7

A new type of test, Generation A, was given to 500 individuals with suspected diabetes, of whom 320 were actually found to have diabetes. The results of the examination are presented in the following table:

Generation A Result

Diabetes

Test Result

Present

Absent

Positive

300

50

Negative

20

130

Compute the sensitivity and specificity of the findings shown for Test A.

a.

Sensitivity = 93.7%, Specificity = 72.2%

b.

Sensitivity = 96.7%, Specificity = 70.2%

c.

Sensitivity = 95.7%, Specificity = 76.2%

d.

Sensitivity = 91.7%, Specificity = 78.2%

Question 8

A new type of test, Generation A, was given to 500 individuals with suspected diabetes, of whom 320 were actually found to have diabetes. The results of the examination are presented in the following table:

Generation A Result

Diabetes

Test Result

Present

Absent

Positive

300

50

Negative

20

130

Compute the positive and negative predictive values of the findings shown for the test.

a.

Positive Predictive value = 82.3% , Negative Predictive Value = 87.5%

b.

Positive Predictive value = 85.7% , Negative Predictive Value = 86.7%

c.

Positive Predictive value = 80.1% , Negative Predictive Value = 82.2%

d.

Positive Predictive value = 77.3% , Negative Predictive Value = 79.3%

Question 9

From the following scatter plot, we can say that between y and x there is _______

a.

Perfect positive correlation

b.

Virtually no correlation

c.

Positive correlation

d.

Negative correlation

7 points

Question 10

A Director of Human Resources is exploring employee absenteeism at the INCOVA Hospital. A multiple linear regression analysis was performed using the following variables. The results are presented below.

Variable

Description

Y

number of days absent last fiscal year

x1

commuting distance (in miles)

x2

employee's age (in years)

x3

length of employment at PPP (in years)

Coefficients

Standard Error

t Statistic

p-value

Intercept

6.594146

3.273005

2.014707

0.047671

x1

-0.18019

0.141949

-1.26939

0.208391

x2

0.268156

0.260643

1.028828

0.307005

x3

-2.31068

0.962056

-2.40182

0.018896

R=0.498191

R2=0.248194

Adj R2=0.192089

se = 3.553858

n = 73

What is the regression equation based on this analysis?

a.

Y = 0.18 x1 + 0.27 x2 –0.51 x3

b.

Y = 6.59 – 0.18 x1 + 0.27 x2

c.

Y = 6.59 – 0.18 x1 + 0.27 x2 – 2.31x3

d.

None of the above

Question 11

A Director of Human Resources is exploring employee absenteeism at the INCOVA Hospital. A multiple linear regression analysis was performed using the following variables. The results are presented below.

Variable

Description

Y

number of days absent last fiscal year

x1

commuting distance (in miles)

x2

employee's age (in years)

x3

length of employment at PPP (in years)

Coefficients

Standard Error

t Statistic

p-value

Intercept

6.594146

3.273005

2.014707

0.047671

x1

-0.18019

0.141949

-1.26939

0.208391

x2

0.268156

0.260643

1.028828

0.307005

x3

-2.31068

0.962056

-2.40182

0.018896

R=0.498191

R2=0.248194

Adj R2=0.192089

se = 3.553858

n = 73

Which of the following interpretations is correct?

a.

For every additional year in the employee's age, the average number of absent days in the last year significantly (p-value<0.05) increases by 0.27 days.

b.

For every additional year in employee’s length of employment, the average number of absent days in the last year significantly (p-value<0.05) decreases by 0.51 days.

c.

None of the above is correct.

6 points

Question 12

A Director of Human Resources is exploring employee absenteeism at the INCOVA Hospital. A multiple linear regression analysis was performed using the following variables. The results are presented below.

Variable

Description

Y

number of days absent last fiscal year

x1

commuting distance (in miles)

x2

employee's age (in years)

x3

length of employment at PPP (in years)

Coefficients

Standard Error

t Statistic

p-value

Intercept

6.594146

3.273005

2.014707

0.047671

x1

-0.18019

0.141949

-1.26939

0.208391

x2

0.268156

0.260643

1.028828

0.307005

x3

-2.31068

0.962056

-2.40182

0.018896

R=0.498191

R2=0.248194

Adj R2=0.192089

se = 3.553858

n = 73

Which of the following statements is correct about the R2?

a.

The adjusted R2 value is 0.25. This means that the model explains around 25% of the variation in the average number of days absent in the last year.

b.

The adjusted R2 value is approximately 0.19. This means that the model explains around 19% of the variation in the average number of days absent in the last year.

c.

The adjusted R2 value is 0.50. This means that the model explains around 50% of the variation in the average number of days absent in the last year.

d.

None of the above is correct.

Question 13

The following graph of a time-series data suggests a _______________ trend.

a.

linear

b.

quadratic

c.

cosine

d.

tangential

7 points

Question 14

Fitting a linear trend to 36 monthly data points (January 2000 = 1, February 2000 =2, March 2000 = 3, etc.) produced the following tables.

Coefficients

Standard Error

t Statistic

p-value

Intercept

222.379

67.35824

3.301438

0.002221

x

9.009066

3.17471

2.83776

0.00751

df

SS

MS

F

p-value

Regression

1

315319.3

315319.3

8.052885

0.007607

Residual

34

1331306

39156.07

Total

35

1646626

The projected trend value for January 2003 is ________.

a.

231.39

b.

555.71

c.

339.50

d.

447.76

6 points

Question 15

Using a three-month moving average, the forecast value for November in the following time series is ____________.

July

5

Aug

11

Sept

13

Oct

6

a.

11.60

b.

10.00

c.

9.67

d.

8.60

6 points

Question 16

When forecasting with exponential smoothing, data from previous periods is _________.

a.

given equal importance

b.

given exponentially increasing importance

c.

ignored

d.

given exponentially decreasing importance

Question 17


A time series with forecast values and error terms is presented in the following table. The mean absolute deviation (MAD) for this forecast is ___________.

Explanation & Answer:
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