TSTA602 – Quantitative Methods for Accounting & Finance

Individual Assignment 1

Unit: TSTA602 – Quantitative Methods for Accounting &
Saturday, 08/08/2020 (03:00 pm)
Due Date:
Number of Questions:
Total Marks:
Four (4) Questions
Twenty (20) marks
All questions should be attempted.
The marks of each question would be awarded based on

your understanding of the questions, concepts and
procedures; hence you should demonstrate your answers
step by step.

Question 1
Part a)
(4 marks)
A sample of n=16 observations is drawn from a normal population with µ=1000 and
σ=200. Find the following.
P(X >1050)
P(960<X <1050)

Part b)
An automatic machine in a manufacturing process is operating properly if the lengths
of an important subcomponent are normally distributed with mean=117cm and standard
deviation =5.2 cm.

Find the probability that one selected subcomponent is longer than 120cm.
Find the probability that if four subcomponents are randomly selected, their mean
length exceeds 120cm.
Question 2
Part a)
(6 marks)

Calculate the statistic, set up the rejection region, interpret the result, and draw the
sampling distribution.
Part b)
H0: µ=10
H1: µ≠10
Given that: σ=10, n=100, X =13, α=0.05.
H0: µ=50
H1: µ<50
Given that: σ=15, n=100, X =48, α=0.05.
A statistics practitioner is in the process of testing to determine whether is enough
evidence to infer that the population mean is different from 180. She calculated the
mean and standard deviation of a sample of 200 observations as X =175 and s=22.
Calculate the value of the test statistic of the test required to determine whether there is
enough evidence to infer at the 5% significance level that the population mean is
different from 180.

Question 3
Part a)
(4 marks)

The mean of a sample of 25 was calculated as mean of 500. The sample was
randomly drawn from a population whose standard deviation is 15. Estimate the
population means with 99% confidence.
Part b)
A random sample of 5 observations was drawn from a normal population. The sample
same and standard deviation are X =175 and s=30. Estimate the population mean with
90% confidence.
Question 4 (6 marks)
Test the following hypotheses of the difference in population means by using the
following data (α = .10)
H0: µ1- µ2=0, Ha: µ1- µ2 <0

Sample 1 Sample 2
X =53.2
X =51.3
σ2=52 σ2=60
n=31 n=32

Use the critical value method to find the critical difference in the mean values
required to reject the null hypothesis.

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