B SEAT NUMBER: ROOM:MACQUARIEUniversity FAMILY NAME: This question paper must be returned. Candidates are not permitted to remove any part of it from the examination room. OTHER NAMES: STUDENT NUMBER: MACQUARIE UNIVERSITY INTERNATIONAL COLLEGE FORMAL EXAMINATION PERIOD: TERM 2, 2018 Unit Code: WSTA150 Unit Name: Business Statistics Duration of Exam (including reading time if applicable): 2 (two) hours plus 10 (ten) minutes reading time Total No. of Questions: 5 (Five) questions Total No. of Pages 15 (fifteen) pages(including this cover sheet): GENERAL INSTRUCTIONS TO STUDENTS: • Students are required to follow directions given by the Final Examination Supervisor and must refrain from communicating in any way with another student once they have enterec the final examination venue. • Students may not write or mark the exam materials in any way during reading time. • Students may only access authorised materials during this examination. A list of authorised material is available on this cover sheet. • All watches must be removed and placed at the top of the exam desk and must remain there for the duration of the exam. All alarms, notifications and alerts must be switched off. • Students are not permitted to leave the exam room during the first hour (excluding reading time) and during the last 15 minutes of the examination. • If it is alleged you have breached these rules at any time during the examination, the matter may be reported to a University Discipline Committee for determination. EXAMINATION INSTRUCTIONS: 1. Write your Student ID number, Name and Surname and table number in the spaces provided at the top of this page. 2. Place your Macquarie University Campus Card in the top right hand corner of your desk, with your photograph facing upwards. 3. You must follow all instructions provided by the ExaminationInvigilators. 4. DO NOT open this examination paper or write anything until the Examination Supervisor instructs you to do so. 5. This paper consists of the following questions: Question Type of Question Content Tested Marks Allocated Instructions 1 20 marks Answers to short answer/calculation questions must be written in the spaces provided after each question. 2 15 marks Questions may be on any content covered in this unit. Short answer/calculation questions3 10 marks 4 20 marks 5 10 marks Exam TOTAL 5 questions 75 marks 6. Attempt ALL questions in this paper as per instructions provided. 7. Write your answers using a blue or black pen (answers in pencil will not be marked). 8. Additional writing space is available on the last two pages of the paper. If you use this space you must indicate which question you are answering. 9. No marks will be awarded for unlabelled or illegible work. 10. If you have a question raise your hand and the Examination Invigilator will approachyou. AIDS AND MATERIALS PERMITTED/NOT PERMITTED: No dictionaries permitted. Non-programmable calculators without text retrieval abi ...

1. B SEAT NUMBER: ROOM:MACQUARIEUniversity
FAMILY NAME:
This question paper must be returned.
Candidates are not permitted to remove any part
of it from the examination room.
OTHER NAMES:
STUDENT NUMBER:
MACQUARIE UNIVERSITY INTERNATIONAL COLLEGE
FORMAL EXAMINATION PERIOD: TERM 2, 2018
Unit Code: WSTA150
Unit Name: Business Statistics
Duration of Exam
(including reading time if applicable): 2 (two) hours plus 10
(ten) minutes reading time
Total No. of Questions: 5 (Five) questions
Total No. of Pages 15 (fifteen) pages(including this cover
sheet):
GENERAL INSTRUCTIONS TO STUDENTS:
• Students are required to follow directions given by the Final
Examination Supervisor and must refrain from communicating
in any way with another student once they have enterec
the final examination venue.

2. • Students may not write or mark the exam materials in any way
during reading time.
• Students may only access authorised materials during this
examination. A list of authorised material is available on this
cover sheet.
• All watches must be removed and placed at the top of the
exam desk and must remain there for the duration of the exam.
All alarms, notifications and alerts must be switched off.
• Students are not permitted to leave the exam room during the
first hour (excluding reading time) and during the last 15
minutes of the examination.
• If it is alleged you have breached these rules at any time
during the examination, the matter may be reported to a
University Discipline Committee for determination.
EXAMINATION INSTRUCTIONS:
1. Write your Student ID number, Name and Surname and table
number in the spaces provided at the top of
this page.
2. Place your Macquarie University Campus Card in the top
right hand corner of your desk, with your
photograph facing upwards.
3. You must follow all instructions provided by the
ExaminationInvigilators.
4. DO NOT open this examination paper or write anything until
the Examination Supervisor instructs you to
do so.
5. This paper consists of the following questions:
Question Type of Question Content Tested Marks Allocated
Instructions
1 20 marks Answers to short

3. answer/calculation
questions must be
written in the spaces
provided after each
question.
2 15 marks
Questions may be on any
content covered in this unit.
Short answer/calculation
questions3 10 marks
4 20 marks
5 10 marks
Exam TOTAL 5 questions 75 marks
6. Attempt ALL questions in this paper as per instructions
provided.
7. Write your answers using a blue or black pen (answers in
pencil will not be marked).
8. Additional writing space is available on the last two pages of
the paper. If you use this space you must
indicate which question you are answering.
9. No marks will be awarded for unlabelled or illegible work.
10. If you have a question raise your hand and the Examination
Invigilator will approachyou.
AIDS AND MATERIALS PERMITTED/NOT PERMITTED:
No dictionaries permitted.
Non-programmable calculators without text retrieval abilities,
and calculators without “run”, “exe” or
“calc” keys are permitted.
A page of formulae and relevant Excel output are included in
the final examination. Students are

4. permitted to take one A4 sheet (any colour), handwritten on
both sides (using pens and/or pencils)
into the final examination. This sheet must be submitted with
the final exam paper at the conclusion of
the exam.
Candidates must supply their own materials as these will not be
supplied at the examination venue. Materials permitted in
the examination may not be shared among students.
Dictionaries:
Calculators:
Other:
Page 1 of 15
Question 1 (20 marks)
a. Suppose the length of time it takes one variety of plant seeds
to germinate is a normally distributed
random variable with a mean of 15 days and a standard
deviation of 4 days. Using the appropriate
Excel code, as provided below, answer the following questions:
Code Result Code Result
NORM.DIST(12, 15 ,4, TRUE) 0.2266 NORM.DIST(1,0,1,
TRUE) 0.8413
NORM.DIST(19, 15, 4, TRUE) 0.8413 NORM.DIST(2,0,1,
TRUE) 0.9772
NORM.DIST(18, 15, 4, TRUE) 0.7733 NORM.DIST(3,0,1,
TRUE) 0.9987
NORM.DIST(9,15,4, TRUE) 0.0668 NORM.INV(0.25, 15, 4)

5. 12.3020
NORM.INV(0.90, 15, 4) 20.1262 NORM.INV(0.75, 15, 4)
17.6979
i) Find the probability that the seed should germinate within 19
days and shade the area of interest
on the bell curve. (3 marks)
ii) Find the probability that the seed should germinate in 12 or
more days and shade the area of
interest on the bell curve. (3 marks)
iii) Find the probability that the seed should germinate between
will be between 12 and 18 days and
shade the area of interest on the bell curve. (4 marks)
Page 2 of 15
iv) By what day should three-fourths of the seeds have
germinated and shade the area of interest
on the bell curve. (3 marks)
v) Based on previous experience by the 15th day 60% of the
seeds germinate. To test this claim a
researcher selected a random sample of 50 seeds and found that
33 seeds germinated by the
15th day. Carry out an appropriate hypothesis test on the
research question below.
Use the following Excel code for this part:
NORM.DIST(0.8660,0,1,TRUE)=0.8068
(7 marks)
Research Question: Was the proportion of seeds germinated by

6. the 15th day equal to 60%?
Page 3 of 15
Question 2 (15 marks)
Research Question: Was the average waiting time for cancer
surgery equal to 16 days, on
average?
The administrators, at hospitals across Australia, claim that the
average waiting time for cancer
surgery is equal to 16 days, on average. Based on discussions
you have had with friends, who
have visited hospital for cancer surgery recently, you dispute
the administrators’ claim.
An independent expert is appointed to test the claim made by
the administrators. Over the course
of a few weekends the expert records the waiting time for 36
randomly selected patients. The
average waiting time for these 36 patients is 15.42 days with a
standard deviation of 6 days.
The following chart and Excel output were produced using the
sample patients’ data gathered for
the study:
Summary statistics
Count Standard deviationMean
36 15.42 6
Histogram for cancer surgery data

7. 12 -i
10 -
& 8 -
T
ELL
4 -
2 -
0 -1
r T T T T T 1
0 5 10 15 20 25 30
waiting time (days)
Excel Command Result
t.dist.2t(0.58,36) 0.5655
t.dist.2t(0.58,35) 0.5656
norm.s.dist(0.58,TRUE) 0.7190
t.inv.2t(0.05,35) 2.0301
Page 4 of 15
(a) Perform an appropriate hypothesis test to validate the claim
by the administrators at 5% level of

8. significance. (10 marks)
(b) Calculate a 95% confidence interval (C.I.) for the average
waiting time (days) for cancer surgery and
interpret the result. (5 marks)
Page 5 of 15
Question 3 (10 marks)
Research Question: Is there a difference between the average
waiting time (AWT) for cancer surgery
(CS) in New South Wales and Victoria?
An independent expert is appointed to test the claim made by
administrators from hospitals across
Australia in Question 2. Over the course of a few weekends the
expert records the waiting time
for 36 randomly selected patients from each state. Use the
following output to answer the research
question:
Histogram tor cancer surgery (VIC)
Histogram tor cancer surgery (NSW)Box plot for cancer surgery
waiting time (days)
12 1
15 "I25 - 10 -
I J e - I 10I- !
I
s -K 10 -

9. 2 -5 -
0 J0 J
5 10 15 30 25i ; ■ 10 15 20 25 30
waiting time (days)waiting time (days)
Test 1
t-Test: Two-Sample Assuming Equal Variances
AWT (NSW) AWT (VIC)
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
15.4444
43.7397
13.8056
19.9325
36 36
31.8361
0
df 70
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail

10. 1.2323
0.1110
1.6669
0.2220
1.9944
Test 2
t-Test: Paired Two Sample for Means
AWT (NSW) AWT (VIC)
Mean
Variance
Observations
Pearson Correlation
Hypothesized Mean Difference
15.4444
43.7397
13.8056
19.9325
36 36
-0.1625
0
df 35
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
1.1488
0.1292

11. 1.6896
0.2584
2.0301
Page 6 of 15
(a) There are two different hypothesis tests, which is the most
appropriate test (Test 1 or Test 2) for
answering the research question above? Explain your choice. (2
marks)
(b) Carry out an appropriate hypothesis test to address the
research question above.
(8 marks)
Page 7 of 15
Question 4 (20 marks)
A study was undertaken by MUIC to investigate the relationship
between the class size (number of
students) and the academic performance of students in the unit
WSTA150 Business Statistics. A random
sample of 15 classes was selected, which included the class size
(number of students) and the average
marks per class (out of 100). The following chart and Excel
output were produced using the sample data.
Use this information to answer the questions which follow:
Scatter Plot Class Size Residual Plot
Histogram for Residuals
7

12. 6
5>u
4
3CTu 3
LL.
2
1
0
-1.8464 -0.7761 0.2941 More
Bin
Table 1:
Regression Statistics
Multiple R 0.9574
R Square 0.9167
Adjusted R Square 0.9103
Standard Error 2.0237
Observations 15
Coefficients Standard Error t Stat P-value
Intercept 91.1918 1.8261 49.9375 0.0001
Class Size -1.0568 0.0884 ***** 0.0002
Page 8 of 15
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(a) Examine the scatter plot and correctly assess the strength
and the nature of the relationship
between the class size and average marks. (2 marks)
(b) Comment on the model assumption, in relation to the
normality of the residuals, by examining
the appropriate plot. (2 marks)
(c) Has the assumption of constant spread of residuals been
met? State which plot you need to
examine for testing this assumption and the reason for your
conclusion. (2 marks)
(d) Calculate the correlation coefficient for the regression
equation, ensure you include the

17. appropriate sign. Interpret the value of this coefficient. (2
marks)
(e) What is the value of the coefficient of determination for the
relationship between the class size
and the average marks obtained by the students. Interpret this
value accurately and in a
meaningful way. (2 marks)
Page 9 of 15
(f) Write down the least squares regression equation and
correctly interpret the equation. (2 marks)
(g) By using the regression equation from part (f) predict the
average marks in WSTA150 for a class
size of 20. (2 marks)
(h) Using the regression equation predict the average marks for
a class size of 3. (1 marks)
(i) Undertake an appropriate test for determining whether the
average marks and the class size are
significantly related (a = 0.05). When answering this question,
you may assume that all assumptions
in relation to the least square regression have been met. (5
marks)
Page 10 of 15
Question 5 (10 marks)
Prior to the 2018 winter Olympics in Pyeongchang, South

18. Korea, various broadcasters and sports
agencies used qualifying times to predict the number of Gold
medals that each country might be
expected to win. One agency predicted that the Norway would
win 20% of the gold medals,
Germany would win 9% of the gold medals, Canada and USA
would each win 6% of the gold
medals and Netherland would win 5% of the gold medals, with
other countries winning the
remainder of the medals. The actual number of medals won is
shown in the Table below:
Number of gold medals won by each country in the 2018 winter
Olympics
Country Norway Germany Canada USA Netherland Other
countries
Total
Gold
medals
won
14 14 11 9 8 47 103
Use a suitable hypothesis test to answer the following research
question. Note that the p-value
for this test is =CHISQ.DIST.RT(12.487,5)=0.029.
Research Question: Among the countries competing at the 2018
winter Olympics did the Norway
win 20% of the gold medals, Germany win 9% of the gold
medals, Canada and USA each win 6%
of the gold medals and Netherland win 5% of the gold medals?
Page 11 of 15

19. This space is for the answer to Question 5.
Page 12 of 15
ADDITIONAL WRITING SPACE
If you use this space you must label your work.
Page 13 of 15
ADDITIONAL WRITING SPACE
If you use this space you must label your work.
END OF EXAMINATION PAPER
Page 14 of 15
m MACQUARIE
University
WSTA 150 Statistical Formulas
y-py-p (for individuals) (for means)
a/Vn
P-P (for proportions) y = za + pz J?

20. a s
standard error (se) of y =
n
estimated se of y =
n
pqse of p = Jv estimated se of p = p
95% CI: p ± 1.96p-pz =
J?
„ = y-p o 95% CI: y±1.96ff
y-p o 95% CI: y±tv-1, (df: v = n-1)t =
s/Vn
yg-Po
95% CI: ^±^7=, (df: v = nd-1)t = sg/T^g
95% CI: (y! - y2) ± tvspJIlp=, (df: v =n± + n2-2)
SpJn1+n2
1 1
+t =
ni n-2
(ni - 1)s^ + (n2 - 1)s^
sp = n1+n2 — 2
bi (df: v = n-2) 95% CI: b1 ± tn-2se(b1)t =

21. se(bi)’
c (ObSj - Exp j )2
XI 2 = Z (df: v = c-1)
j=i Exp j
c (ObSj - Exp jj )2
x2 =S-=i z (df: v = (r-1)(c-1) )
j=i Expij
Page 15 of 15