Online Supplementary Assessment for HI6007 Statistics for Business Decisions

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HI6007
Statistics for Business Decisions
Online Supplementary Assessment
Trimester 3, 2020
Assessment Weight: 50 total marks
Instructions:
 All questions must be answered by using the answer boxes provided in this paper.
 Formula Sheet is included with this paper
 Completed answers must be submitted to Blackboard by the published due date
and time. Submission instructions are at the bottom of this paper.
Purpose:
This assessment consists of six (6) questions and is designed to assess your level of
knowledge of the key topics covered in this unit
HI6007 Online Supp T3 2020

HI6007 Online Supp T3 2020

Question 1 (7 marks)
APT Accounting and tax consultancy provide various services, including tax, mortgage, book keeping,
audit and personal financial planning. They have examined the behavior of their clients. Based on the
experience, they estimate that 10% of their clients seek help for mortgages and 5% for personal
financial planning. Of those who seek help for mortgages, 40% also seek help for personal financial
planning.
a) What percentage of the clients seek help for both mortgages and personal financial
planning? (4 marks)
ANSWER: ** Answer box will enlarge as you type
P(mortgages) = 6%
P(Personal finance) = 5%
P(Both mortgages and personal finance) = 10% - 40% = 4%
b) What percentage of the clients do not seek help for either of these two services? (3marks)
ANSWER:
Total
population= 10% +5% = 15%
Percentage of clients no seeking either of these two services = 6%+5%-4% = 7%.
= 15% - 7% = 8%
Question 2 (7 marks)
HI6007 Statistics for Business Decisions T3 2019 final exam marks were normally distributed with a
mean of 78 and a standard deviation of 6.
a) Estimate the proportion of the class that has a final exam mark of less than 75 (3 marks)
ANSWER:
z = (x-mean)/standard deviation
= (75-78)/6 = -0.5 = P(z<-0.5)
= (0.3085)
b) Calculate the probability that a class of 50 has an average final exam mark that is less than 75
(4 marks)
ANSWER:
If class is of 50 students, the students having average marks of less than 75
= 0.3085*50 = (15.425)
HI6007 Online Supp T3 2020

Question 3 (11 marks)
According to the Annual survey of drugs expenditure in country X, the annual expenditure for
prescription drugs is $838 per person in the Northeast region of the country. A sample of 60
individuals in the Midwest shows a per person expenditure for prescription drugs of $745. Further, it
is given that the population standard deviation of $300.
a) Formulate hypotheses for a test to determine whether the sample data support the
conclusion that the population annual expenditure for prescription drugs per person is lower
in the Midwest than in the Northeast and Identify whether it is a two-tail test or a one tail
test (Left or right tail) (3 marks)
ANSWER:
N (size of sample) = 60
Sample mwean = $745
Standard deviation of population = $300
H0 = μ = $838
Hα = μ < $838
b) Decide the suitable test statistics and justify your selection (1 mark)
ANSWER:
Z = (Sample mean – Population mean) / (Standard deviation / square root of n)
= (745 – 838) / 300 / square root of 60
Z = -2.40
c) Calculate the value of the relevant test statistics and identify the P value (3 marks)
ANSWER:
P value = P(Z<-2.40)
P = 0.0082
d) Based on the p value in part (III), at 99% confidence level, decide the decision criteria (1
mark)
ANSWER:
P value = 0.0082 < α = 0.01
By taking into account outcomit can be stated that alternative hypothesis is true and other one false.
e) Make the final conclusion based on the analysis (3 marks)
ANSWER:
Referring statistical evaluation it can be presented that annual expenditure pertaining to drugs per
person is lower in Midwest as compared to Northeast.
HI6007 Online Supp T3 2020