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MATH1015
Biostatistics
Lecturers:
Time Allowed: Reading - 10 minutes; Writing - 1.5 hours
Exam Conditions: This is a closed-book examination — no material permitted. Writing
is not permitted at all during reading time.
This examination has two sections: Multiple Choice and Extended Answer.
The Multiple Choice Section is worth 50% of the total examination.
There are 20 questions. The questions are of equal value.
All questions may be attempted.
Answers to the Multiple Choice questions must be entered on
the Multiple Choice Answer Sheet before the end of the examination.
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.
THE QUESTION PAPER MUST NOT BE REMOVED FROM THE
EXAMINATION ROOM.
Marker’s use
only
Page 1 of 20
Sample Exam Questions A 2018 Page 2 of 20
Multiple Choice Section
In each question, choose at most one option.
Your answers must be entered on the Multiple Choice Answer Sheet.
1. In a medical trial, the placebo effect occurs when
(a) the subject is scared of the trial
(b) the subject responds to the idea of the treatment
(c) the subject is already sick
(d) the subject knows the investigator
(e) there is a historical treatment group
2. In a study on smoking and lung cancer, a possible confounder is NOT
(a) a gene for smoking (b) brand of cigarettes (c) diet
(d) alcohol (e) exercise
3. Simpson’s Paradox occurs when
(a) relationships between percentages in subgroups are reversed when the subgroups are
combined.
(b) relationships between percentages in subgroups are the same when the subgroups
are combined.
(c) relationships between percentages in subgroups are the same when the subgroups
are separated.
(d) relationships between percentages in subgroups disappear when the subgroups are
separated.
(e) a clear trend in individual groups of data is revealed when the groups are pooled
together.
4. Suppose a set of bivariate data has a correlation coefficient of 0.90. Which statement is
true?
(a) 90% of the points are highly correlated.
(b) 90% of the points fall on a line.
(c) The linear regression line has a slope of 0.9.
(d) 90% of the points can be predicted by a linear regression line.
(e) The data may have a strong linear trend.
5. In a dataset of size 6, the mean is 7 and standard deviation is 4. We add 3 to each
observation in the data. The new mean and standard deviation are respectively
(a) 7 and 4 (b) 10 and 4 (c) 10 and 7 (d) 7 and 7 (e) 10 and 13
Sample Exam Questions A 2018 Page 3 of 20
6. A box has a mean 7 and standard deviation 2. Which distribution can best approximate
the distribution for the mean of 100 draws?
(a) Normal with mean 7 and standard deviation 2.
(b) Normal with mean 7 and standard deviation 0.2.
(c) Normal with mean 700 and standard deviation 20.
(d) T with degrees of freedom 99, mean 7 and standard deviation 2.
(e) T with degrees of freedom 100, mean 700 and standard deviation 20.
7. For a quantitative data set, the mean and median are the same. Which statement is
true?
(a) The histogram is skewed (b) The scatterplot shows a linear trend
(c) The barplot is balanced (d) The boxplot is symmetric
(e) not enough information
8. For a quantitative data set, the interquartile range (iqr) is 1. Which statement is true?
(a) The data is skewed. (b) There is no outlier.
(c) The standard deviation is 1. (d) The boxplot has length 1.
(e) The box in the boxplot has length 1.
9. If Z ∼ N(0, 1) then P (−3 ≤ Z ≤ 3) is closest to
(a) 0.25 (b) 0.5 (c) 0.68 (d) 0.95 (e) 0.997
10. Which is the output for the following R command?
pnorm(0)
(a) 0 (b) 0.5 (c) 0.7 (d) 0.9 (e) 1
11. Using the linear regression line, what expression would predict y when x = 2.
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 1.8403 0.8655
(a) 1.8403− 0.8655× 2 (b) 1.8403 + 0.8655× 2 (c) 0.8655 + 1.8403× 2
(d) 0.8655− 1.8403× 2 (e) Not enough information
Sample Exam Questions A 2018 Page 4 of 20
12. A box contains the numbers 0,2,3,4,6 and 25 draws are made with replacement. The
expected sum of draws and the standard error are respectively
library(multicon)
box=c(0,2,3,4,6)
mean(box)
## [1] 3
popsd(box)
## [1] 2
(a) 3/25 and 2/
√
25 (b) 3×
√
25 and 2/
√
25 (c) 3×
√
25 and 2×
√
25
(d) 3× 25 and 2×
√
25 (e) 3× 25 and 2× 25
13. A box contains the numbers 0,2,3,4,6 and 100 draws are made with replacement. Which
R codes calculate the probability that the mean of draws lies within 2.9 to 3.1?
(a) pnorm((3.1-3)/(2*10))-pnorm((2.9-3)/(2*10))
(b) pnorm((3.1-3)/(2/100))-pnorm((2.9-3)/(2/100))
(c) pnorm((3.1-3)/(2/10))-pnorm((2.9-3)/(2/10))
(d) pnorm((2.9-3)/(2/10))-pnorm((3.1-3)/(2/10))
(e) pt((3.1-3)/(2/100),100)-pt((2.9-3)/(2/100),100)
14. A box contains the numbers 0,2,3,4,6, each repeated 200 times and 20 draws are made
without replacement, which of the following statements about standard error for the
sum of draws is TRUE?
(a) It becomes one fourth if the sample size is half.
(b) It drops to 0 if the sample size is 200.
(c) It remains unchanged compared to the with replacement case.
(d) It enlarges by a factor of
1000− 20
1000− 1 compared to the with replacement case.
(e) It shrinks by a factor of
√
1000− 20
1000− 1 compared to the with replacement case.
15. A box contains nine “0” and one “1” and 16 draws are made with replacement. Which
distribution will best approximate the distribution for the average of draws?
box=c(0,0,0,0,0,0,0,0,0,1)
library(multicon)
mean(box)
## [1] 0.1
Sample Exam Questions A 2018 Page 5 of 20
popsd(box)
## [1] 0.3
(a) Normal with mean 0.025 and standard deviation 0.3/4.
(b) Normal with mean 0.1 and standard deviation 0.3/16.
(c) T with degrees of freedom 15, mean 1.6 and standard deviation 0.3*4.
(d) Unknown skew distribution with mean 0.1 and standard deviation 0.3/4.
(e) Unknown skew distribution with mean 0.4 and standard 0.3*4
16. A box contains nine “0” and one “1” and 16 draws are made with replacement. Using
the simulation result below, what is the probability that the sum of draws is at least 6?
box=c(0,0,0,0,0,0,0,0,0,1)
sim=replicate(10000,sum(sample(box,16,rep=T)))
table(sim)
## sim
## 0 1 2 3 4 5 6 7
## 1840 3382 2667 1416 533 134 26 2
(a) 0.0002 (b) 0.0026 (c) 0.0028 (d) 0.1840 (e) 0.9998
17. A marketing company is surveying consumers’ preference for Coke over Pepsi. If p =
P (Customer prefers Coke to Pepsi), the null and alternative hypotheses are respectively
(a) H0 : p = 0.5 and H1 : p 6= 0.5 (b) H0 : p = 0.5 and H1 : p > 0.5
(c) H0 : p 6= 0.5 and H1 : p = 0.5 (d) H0 : p = 0.5 and H1 : p < 0.5
(e) H0 : p < 0.5 and H1 : p > 0.5
18. A marketing company is surveying consumers’ preference for Coke over Pepsi. Which
box could NOT model the null hypothesis?
(a) 0,1 (b) 0,1,1 (c) 0,0,1,1 (d) 0,0,0,1,1,1 (e) 0,0,0,0,1,1,1,1
19. A marketing company is surveying consumers’ preference for Coke over Pepsi. Out of
100 consumers surveyed, 60 prefer Coke to Pepsi. Which formula gives the test statistic?
box=c(0,1)
mean(box)
## [1] 0.5
Sample Exam Questions A 2018 Page 6 of 20
popsd(box)
## [1] 0.5
(a)
60− 50
10
(b)
50− 0.6
10
(c)
0.6− 0.5
0.05
(d)
0.6− 0.5
0.5
(e)
0.5− 0.6
5
20. A test was conducted to test the hypotheses H0 : µA = µB vs H1 : µA 6= µB where µA
and µB represent the population mean for group A and B respectively.
##
## Welch Two Sample t-test
##
## data: yield by variety
## t = -4.9994, df = 19.441, p-value = 7.458e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.9293569 -0.3814274
## sample estimates:
## mean in group A mean in group B
## 4.052941 4.708333
Based on the results above, which of the following statements is FALSE?
(a) The test statistic is -4.9994.
(b) The p-value is close to zero.
(c) Equality of variance assumption is made.
(d) The data are against H0.
(e) The 95% confidence interval of µA − µB excludes 0.
End of Multiple Choice Section
Make sure that your answers are entered on the Multiple Choice Answer Sheet
The Extended Answer Section begins on the next page
Sample Exam Questions A 2018 Page 7 of 20
Extended Answer Section
Answer these questions in the spaces provided.
1. We are interested in monitoring the air quality index (AQI) in the month of July 2015
between two regions: Sydney’s central-east (CE) and Sydney’s north-west (NW). Due
to the fact that data readings from different pollutants have different underlying units
of measure, the AQI is a derived value based on multiple data readings that enables
easier comparison across regions and time. In general an AQI score above 100 and
below 150 indicates a ‘poor’ air quality level and that people in the sensitive group (e.g.
people with asthma, older adults and children) should consider either cutting back or
rescheduling strenuous outdoor activities. The general public are usually not affected
by the air quality within this AQI range.
Source: http://www.environment.nsw.gov.au/AQMS/search.htm
head(data)
CEAQI NWAQI
[1,] 99 92
[2,] 32 44
[3,] 70 82
[4,] 74 96
[5,] 95 100
...
[29,] 41 59
[30,] 48 57
[31,] 34 58
CE=data$CEAQI
NW=data$NWAQI
summary(CE)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 30.00 35.50 41.00 50.77 60.50 108.00
summary(NW)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 33.00 38.50 54.00 56.52 67.00 100.00
n = nrow(data)
table(CE >= 100)
## FALSE TRUE
## 30 1
Sample Exam Questions A 2018 Page 8 of 20
table(NW >= 100)
## FALSE TRUE
## 30 1
l lCE
N
W
40 60 80 100
l
l
l
l
l
l
l
l
l
l
l
lll l l
l
l
l
l
l
ll
l
ll
ll l
l
40 60 80 100
40
50
60
70
80
90
10
0
CE
N
W
Look over the R output and then answer the following questions.
(a) Begin by examining the air quality index (AQI) of Sydney’s central-east (CE) region.
(i) What is the mean AQI score for Sydney’s CE region during July?
(ii) Comment on the shape of the boxplot for Sydney’s CE region during July.
(iii) Would it be better to report the mean or median as the measure of centre for
Sydney’s CE region? Explain.
(iv) How many days in July was the air quality considered ‘poor’ in Sydney’s CE
region?
Sample Exam Questions A 2018 Page 9 of 20
(b) The scatter plot graphically shows the air quality index (AQI) relationship between
the two Sydney regions in the month of July.
(i) From the scatter plot, suggest a value for the correlation coefficient between
the two Sydney regions. Explain what it represents.
(ii) Suppose on the 28th of July, the air quality monitoring instrument was not
working in Sydney’s NW region, but the AQI value in Sydney’s CE region
was recorded as 40. Using the R output below, give an expression without
evaluation to estimate the AQI value in Sydney’s NW region.