Mathematics Assignment Answers with Solutions

This document contains answers to various Mathematics assignments including relative risk, statistical tests, screening programs, and more. It also includes explanations and calculations for each answer. The subject is Mathematics and the course code and college/university are not mentioned.

Mathematics
Student Name:
Instructor Name:
Course Number:
6 August 2018

Answers
Q1: C
Q2:
a. C
b. Answer below;
Baseline body Number of
incident cases
of colon cancer
Person-years
Crude incidence
rate/100,000 Person
Yearmass index* of follow up
<22 35 53,070 65.95
22 - <24 38 38,510 98.68
24 - <26 23 36,210 63.52
26 - <28 76 32,330 235.08
28 - <30 43 21,020 204.57
30+ 69 34,700 198.85
The group with the highest incidence rate was those between 26- <28 while the group with the
lowest incidence rate was the 24- <26 group.
c. Answer below;
The relative risk (RR), its standard error and 95% confidence interval are calculated according to
Altman, 1991.
The relative risk or risk ratio is given by
RR= 3.1018
The relative risk is 3.1018; this suggests that there is an increased risk of colon cancer associated
with a BMI of 28 - <30 as compared to the lowest BMI category.
Q3:
a. The value of the intercept is 38
b. The value shows that holding x constant (zero value for x) we would expect the SBP to be 38
c. The value of the slope is 0.9
d. The value of the slope shows that a unit increase in x would result to an increase in the SBP
by 0.9. Similarly, a unit decrease in x would result to a decrease in the SBP by 0.9

Q4: C
Q5:
a. Relative risk is given as follows;
RR= a /(a+b)
c /(c+ d)= 205/100,000
42 /100,000 =4.88
b. Risk difference is given as follows;
RD= a
a+b − c
c+ d → 205
100000 − 42
100000 = 163
100000 =0.00163
Q6:
a. Statistical test is Kruskal–Wallis test
Q7: Discuss the criteria for a successful screening program?
 The disease produces substantial death and/or disability
 Early detection is possible & improves the outcome
 There is a feasible testing strategy for screening
 Screening is acceptable in terms of harms, costs, & patient acceptance
Q8:
a. The resulting odds ratio of 3.4 means that the odds of breast cancer in smokers is estimated to
be 3.4 times the odds of breast cancer in non-smokers. While the 95% confidence interval for
the odds ratio shows that this odds ratio is between 2.4 and 4.8.
b. We conclude that smoking is most likely to be a risk factor for the breast cancer. This is because
the smokers are 3.4 times likely to have breast cancer as compared to non-smokers.
Q9: A
Q10: A; this is because it is a rare disease
Q11: A
Q12: C
Q13: B; The event rates in each age stratum in the standard population are used to create a weighted
average rate
Q14:
The coefficient of determination is 0.49; this implies that the percentage of variance explained for the
correlation is 49%. This correlation is clinically important since it is a strong positive correlation.
Q15: C
Q16:

a. FALSE
b. TRUE
Q17:
Four factors will be extracted; the four factors have Eigen value greater than 1.
Q18:
The extracted factors (4 factors) will explain 91.6% of the variance. This is found by getting the
cumulative percent for all the factors with Eigen value greater than 1.
Q19:
a. The specific questions that were represented in Factor I are; q1, q2, q6, q7 and q9. This based on
the fact that the said questions have a loading greater than 0.5
b. The specific questions that were represented in Factor II are; q3, q4, q5, q8 and q10. This based
on the fact that the said questions have a loading greater than 0.5.
Q20: D
Q21: Null hypothesis
Q22: C
Q23: A, C and F
Q24: D, F and G
Q25: A and E
Q26:
 Used to reduce a large number of variables into fewer numbers of factors.
 Used to identify underlying Factors
 Used to Screen Variables
Q27:
Yes the scale is internally consistent. The Cronbach alpha value is greater than 0.7 which shows that it is
good.
Q28:
Decision would be to delete item 7 so that the internal consistency of the scale can be improved
significantly.
In conclusion when item 7 is deleted, the Cronbach’s Alpha becomes 0.873 which is close to having an
excellent internal consistency.
Q29: D
Q30:

The above shows that 84% of lung cancer cases is attributable to exposure (asbestos). The implication is
that this proportion (84%) would have been avoided if asbestos was not in the picture.
Q31: A
Q32: A
Q33: C
Q34:
With R-square being 0.70 it implies that 70% of the variation in the dependent variable (diastolic blood
pressure) is explained by height (independent variable) in the model.
Q35: B
Q36: A