Statistics for Managerial Decision - Assignment 2 Analysis Report

This document presents a comprehensive solution to a statistics assignment focused on managerial decision-making. The assignment covers a range of statistical concepts, including quarterly opening prices analysis, stem and leaf displays, graph interpretation (histograms, polygons, and bar charts), and analyst recommendations. It delves into numerical measures such as mean, median, quartiles, standard deviation, and box-whisker plots. The solution also explores probability, including proportions and applications of Poisson and normal distributions. Furthermore, the assignment includes the computation of confidence intervals and analysis of normal probability plots. The document provides detailed calculations, interpretations, and graphical representations to support the statistical analysis, offering valuable insights into data analysis techniques relevant to managerial contexts. This assignment solution is contributed by a student and available on Desklib, a platform providing AI-based study tools for students.

STATISTICS FOR MANAGERIAL DECISION
STUDENT ID:
[Pick the date]

Question 1
(a)Quarterly opening prices and stem and leaf display
(b)Graph (Histogram and polygon)
(c)Bar chart

(d) Based on the analyst recommendations given by Reuters, the preferred stock from the
available options would be one which has a better rating.
SYD Stock: Recommendation
Source: https://www.reuters.com/finance/stocks/analyst/SYD.AX

ALX Stock: Recommendation
Source: https://www.reuters.com/finance/stocks/analyst/ALX.AX
By comparing the average rating on the two stocks, it is apparent that a better rating is visible
on ALX in comparison to SYD since the mean rating for the former is 2.8 as compared to
3.45 for the latter. A lower rating value is preferable.
Question 2
(a) Numerical measures “Mean, Median, First and third Quartile”
(b) Numerical measures “Standard deviation, mean absolute deviation and range”

(c) Box -whisker plot
(d) The information in context of the costs of the given white goods is summarised as
follows.
Annual costs for refrigerator

Annual costs for TV (50 inch LED)
Annual Costs for Washing Machine

Annual Costs for Dryer
Link: https://www.canstarblue.com.au/electricity/costly-appliances-run-home/
Question 3
(a) Proportion (Income from Australia, Taxation) =72670/231942=0.313

(b) Probability(Interest income, environment, Govt. of Queensland) =2429/50119= 0.048
(c) Probability (Money Federal Govt., rail expansion, capital grant to Tas)=67/8162= 0.008
(d) Australian states South Australia(SA) and Victoria (Vic) are in worst and best
positionrespectively (GFS Net Operating Balance).
Question 4
(a) Rainfall - Poisson Distribution
(i) Probability (No rainfall in a week)
Rainfall experienced in year = 182
Average rainfall days per year λ = 182/52 = 3.5
P(X = 0) = 3.50 × e−3.5
0! = 0.030197
(ii) Probability(4 or more days of rainfall in week)
PሺX ≥ 4ሻ= 1 − 3.30773 × e−3.30779
3! = 0.2746
(b) Rainfall - Normal Distribution
(i) Probability (20 mm <rainfall amount < 60 mm)
Mean = 74.89
Standard deviation = 119.21
Standard error =119.21/(52)^0.5 =16.53
(j) P(Rainfall >x)=0.15

z=(x-74.89)/16.53
z value = -1.03643 (From NORMSINV (0.15))
-1.03643=(x-74.89)/16.53
X = 57.76
Rainfall amount=57.76 mm
Question 5
(a) Normal probability plots for variables that has more than 50%non-zero values is shown as
follows.