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Unformatted text preview: 8010A SEMESTER 1 2009 THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS MATH 1015
BIOSTATISTICS June 2009 LECTURER: Dr S Peiris TIME ALLOWED: 90 Minutes This examination has tWO sections: Multiple Choice and Extended Answer. The Multiple Choice Section is worth 50% of the total examination;
there are 30 questions; the questions are of equal value;
all questions may be attempted. Answers to the Multiple Choice questions must be coded onto
the Multiple Choice Answer Sheet. The Extended Answer Section is worth 50% of the total examination;
there are 3 questions; the questions are of equal value;
all questions may be attempted;
working must be shown. \ Calculators will be supplied.
A formula sheet for use in this examination is printed after the last
question in this booklet. Statistical tables will be provided. THE QUESTION PAPER MUST NOT BE REMOVED FROM THE
EXAMINATION ROOM. PAGE 1 OF 16 8010A SEMESTER 1 2009 PAGE 7 OF 16 Extended Answer Section There are three questions in this section, each with a number of parts. Write your answers
in the space provided below each part. If you need more space there are extra pages at the
end of the examination paper. 1. [ J 5 marks] A
(a) An experiment looked at the effect of position on the level of blood pressure. In
the experiment 32 patients had their blood pressures measured While lying down
with their arms at their sides (R) and again standing with their arms supported at
heart level The differences, as = R— S in their systolic blood pressures (Bernard
Rosner, Fundamental of Biostatistics (2006), Thomson p39) are: ~8—6—202244466'68888
5101010121212141414141416182628 Comment on the effect of position on the levels of systolic blood pressures. Obtain
a suitable double stern and leaf plot for these data. Given that Z a: = 282 and Z 9:2 z 4340, ﬁnd the proportion of observations in (11': — 2s, 5% + 23), where a‘: is the sample mean and s is the sample standard deviation. 8010A SEMESTER 1 2009 PAGE 8 OF 16 (b) A surgical procedure can be classiﬁed as unsuccessful (U) or successful (S) with
probabilities P(U)=0.15 and P(S)=O.85. If four patients receive this procedure in turn and their outcomes are independent, compute the probability that the ﬁrst
three are successful and the last one is unsuccessful. What is the probability of having any three of the operations successful? 8010A SEMESTER 1 2009 PAGE 9 OF 16 2. [15 marks] (a) A consumer group claims that the cure rate of a new drug for skin cancer is less
than that of the previous rate of 0.90. To test this a medical team took a random
sample of 280 patients and found that only 240 said they obtained relief using this
medication. Based on a suitable statistical argument verify the consumers claim. 8010A SEMESTER 1 2009 PAGE 10 OF 16 (b) As a part of an experiment in a community counselling center, 42 new clients are
assigned at random to be interviewed by either a student or a stafff clinician. The
variable of interest is the numb er of days, a: between the initial visit and the follow—up
visit. The resulting data are summarized as follows: I n 23 19
5?: 51 46
s 12.8 13.4 Do these data suggest that the mean interval between visits is signiﬁcantly greater
when the interviewer is a student than when the interviewer is a staff member?
Hint: Conduct an appropriate 75 test assuming normality and draw your conclusion
based on the associated Pualue. ‘ 8010A SEMESTER 1 2009 PAGE 11 OF 16 3. [15 marks]
(a) The Clinic of a health plan selects a random sample of records for 20 male members and summarizes the following information on age and the number of visits to
the clinic y) in the past year: Zr = 850,231 = 34, 2:102 = 41128, Zyz = 88
and 2 my 2 1796. Find the correlation between as and y and interpret this value. Find the regression line relating number of visits to the age of the plan member.
Given that a male of 39 years visited the clinic twice, ﬁnd the residual of y When
:1: = 39. 8010A SEMESTER 1 2009 PAGE 12 OF 16 (b) A biologist wants to test the claim that the number of red, white, yellow and pink
ﬂowered plants resulting after cross—pollination follow the ratio l:2:2:5. After cross—
polh'nation of 300 seeds, he obtains the results below: 158 300 Test whether the given model ﬁts the data ﬁts well. End of Extended Answer Section 8010A SEMESTER 1 2009 PAGE 15 OF 16 NOTES FOR USE IN THE STATISTICS EXAMINATION 9 Calculation formulae:
— For a sample 331, 932, . . . ,rn Sample mean, 1% Sample variance, 52 For the regression line
y = a + bx: 9 Some probability results: For any two events A and B PAUB) =P(A)+P(B)—P(AIIB) (
If A and B are mutually exclusive (me) P(A D B) = O and P(A U B) = P(A) + P(B)
(
( If A and B are independent P Am B) = P(A)P(B) and P A o B) = P(A) + P(B) — P(A)P(B) a If X is a discrete random variable, then E(Xk) : ZrkP(X = 7") and Var(X) =
E(X2) — [Emig o If X N 801,19), then P(X = 7‘) = <Z>pr(1 —p)”‘r,r = O,   ,n. It can be Shown that E(X) = 71p, Var‘(X) = np(1 ~— p).
0 Some test statistics and their sampling distributions (under appropriate as—
sumptions and hypotheses): End of Formulae Sheet ...
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