BME 433/533 BIOSTATISTICS Homework #8
Due: Friday 12/3/2023 11:59 PM. State your assumptions where necessary.
1.)
The following table shows the distribution of uric acid determinations taken on 250 patients. Test the
goodness-of-fit of these data to a normal distribution. You may estimate mean and variance as
 k  
  ni  − 1 , where Ci is the center of the bin,
i =1
i =1
i =1
 i =1  
e.g. C1 = 0.5, C2 = 1.5, ...., C11 = 10.5; Let  = 0.05. Give the p-value.
k
x =  Ci ni
k
k
 ni ; s 2 =  (Ci − x )2 ni
Uric Acid
determination
Observed
frequency
Uric Acid
determination
Observed
frequency
<1
1 - 1.99
2 - 2.99
3 - 3.99
4 - 4.99
5 - 5.99
1
5
17
20
43
50
6 - 6.99
7 - 7.99
8 - 8.99
9 - 9.99
10 or higher
47
26
26
10
5
Total:
2.)
250
The face sheet of patients’ records maintained in a local health department contains 10 entries. A sample
of 100 records revealed the following distribution of erroneous entries
Number of erroneous
entries out of 10
Number of records
0
8
1
32
5
2
25
3
24
4
10
5 or more
1
TOTAL
100
Test the goodness-of-fit of these data to the binomial distribution with p = 0.15. Find the p-value.
3.)
A sample of 490 college students participated in a study designed to evaluate the level of college
students’ knowledge of a certain group of common viral diseases. The following table shows the
students classified by major field of study and level of knowledge of the group of diseases
Knowledge of Diseases
Major
Good
Poor
Total
Premedical
34
88
122
Other
19
349
368
Total
53
437
490
Do these data suggest that there is a relationship between knowledge of the group of diseases and major
field of study of the college students from which the present sample was drawn? Let α = 0.05.
4.)
Height, forearm bone size and femur length were measured in 12 males between the ages of 12 and 18
years. Below is the resulting 3x3 covariance matrix.
(all covariances in cm2 )
Height (Y)
Radius Length (X1)
Femur Length (X2)
Height (Y)
Radius Length (X1)
Femur Length (X2)
104.172
18.731
30.655
18.731
3.384
5.54
30.655
5.54
9.079
(a) Find each of the partial correlation coefficients and test each for significance. Let α = 0.05 for all tests.
(b) Determine the p value for each test and state your conclusions.