HA1011 - Applied Quantative methods

APPLIED QUANTITATIVE
METHODS
HA1011
Student Name
[Pick the date]

Question 1
(a) The frequency table is highlighted below:
(b) Histogram
(c) Mean, median and mode of the data
1

Mean
Sample size = 60
Total sum = 62600
Mean = Total sum/ Sample size = (62600/60) = 1033.3
Median
Sorted data in ascending form
2

3

Here,
Median = 715
Mode
The maximum repetition incurred for 401 and therefore, the mode of the data is 401.
Question 2
(a) The given set of data would be categorised as sample not the population. This is because
only the data for the seven weeks has been provided and the given data does not
correspond to all the weeks for which the university is working. Hence, the data would be
sample.
(b) The standard deviation for weekly attendance
4

Sample size = 7
Total sum = 3392
Mean (x bar) = Total sum/ Sample size =3392/7 = 484.57
Standard deviation
Standard deviation = 74.06
(c) IQR (inter quartile range)
5

(d) Calculation of correlation coefficient (r)
6

Question 3
Regression Model
Intercept
Slope
7

Therefore, the regression line equation would
Example to explain the regression equation
 Holmes University has closed which there would be zero weekly attendance.
 When number of students is increased to 10, then the total number of bars sold would also be
enhanced by 1068 units that are same as 10 times number of coefficient of weekly
attendance.
(b) Calculation of coefficient of determination
8

93.70% of deviation in number of chocolate bars sold can be described by deviation in the
weekly attendance.
Question 4
Data and information is shown below:
(a) Probability that a randomly chosen player is receiving grassroots training or is from Holmes
University.
(b) Probability that a randomly chosen player is receiving scientific training and is external.
(c) Probability that a randomly chosen player is receiving scientific training and is from Holmes
University.
9

(d) The objective is to decide whether the two events training and recruitment are considered as
independent variable.
Condition of two events P and Q to be termed as independent events
Let
And,
Result
(e) Condition of two events P and Q to be termed as independent events are not satisfied and
hence, training and recruitment cannot be considered as independent variable.
Question 5
(a)
10

And,
Bayesian Probability
(b) Primary choice of customer will only be product X
Question 6
(a) Probability that 2 or less than 2 customers will purchase from shop
Binomial Distribution
11

Number of trials = 8
Probability of success = 0.1
(b) Probability that in 2 minutes total 9 customers will enter into shop
Poisson distribution
Question 7
(a) Probability that apartment will sell more than $2 million
12

From Standard Normal Table
(b) Probability that apartment will sell over $1 million but lower than $1.1 million
From Standard Normal Table
13

Question 8
(a) For a given sampling distribution to be assumed as normal , it is imperative as per the CLT
(Central Limit Theorem) that the sample size must be large and hence must be greater than
30. The given variable would be considered as normally distributed owing to the sample size
being greater than 30. Therefore, z can be used as the suitable test statistics for checking the
assistant’s findings.
(b) Sample proportion
Total investors = 45
Investors agreed to invest = 11
Standard error
Among the investors, 30% of the investors are ready to participate to make the fund profitable
and to commit an investment of $1 million or more into fund.
From Standard Normal Table
14