Statistics Homework Assignment - University Statistics Course

This document presents a comprehensive solution to a statistics homework assignment, covering a range of statistical concepts and methods. The solution begins with data analysis, including the creation of stem and leaf plots to compare the opening prices of two companies. It then delves into descriptive statistics, calculating means, standard deviations, and quartiles for various retail sectors. Probability calculations are also explored, analyzing internet usage across different regions and calculating probabilities related to specific events. Furthermore, the solution addresses hypothesis testing and confidence intervals, including z-statistic calculations and the determination of confidence intervals for population means. The assignment concludes with a discussion of sampling distributions and the application of statistical methods to real-world scenarios, such as analyzing student attendance and flight booking behavior. The document provides a detailed breakdown of each problem, ensuring a thorough understanding of the statistical principles involved.

Running head: Statistic
Statistics
Name of the student
Name of the university

2Statistic
Table of Contents
Q1...............................................................................................................................................3
Q2...............................................................................................................................................5
Q3...............................................................................................................................................7
Q4...............................................................................................................................................7
Q5...............................................................................................................................................8
References:...............................................................................................................................10

3Statistic
Q1.
a)
Opening prices for companies TLS and TPM
TLS TPM
Jan 3.44 1.63594
2010 Apr 3.01 2.26968
July 3.23 1.86192
Oct 2.64 1.50821
Jan 2.79 1.58681
2011 Apr 2.82 1.65068
July 2.91 1.65559
Oct 3.08 1.35591
Jan 3.33 1.30679
2012 Apr 3.3 1.75876
July 3.7 1.72928
Oct 3.89 2.19108
Jan 4.37 2.54479
2013 Apr 4.51 3.09502
July 4.76 3.43891
Oct 4.97 4.27408
Jan 5.25 5.22714
2014 Apr 5.07 6.42585
July 5.23 5.39418
Oct 5.31 6.66166
Jan 5.97 6.63219
2015 Apr 6.32 9.0689
July 6.12 8.80361
Oct 5.62 10.7491
Jan 5.61 9.71738
2016 Apr 5.27 11.0242
July 5.58 11.6923
Oct 5.2 8.47937
Jan 5.1 6.70096
2017 Apr 4.66 6.868
July 4.33 5.7
Oct 3.49 4.89
Jan 3.63 6.57
2018 Apr 3.14 5.49
July 2.64 5.15
Oct 3.17 8.38

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b) STEM AND LEAF PLOT
TL
S
TP
M
Stem
1 3 4 5 6 7 7 8 9
9 8 8 6 6 2 2 3 5
9 7 6 5 4 3 3 2 2 1 1 3 1 4
8 7 5 4 3 4 3 9
6 6 6 3 3 3 2 2 1 1 5 2 2 4 5 7
3 1 6 4 6 6 7 7 9
7
8 4 5 8
9 1 7
10 7
11 7
12
c)
ALL PCC SGR IEL TTS
0
2000
4000
6000
8000
10000
12000
14000
16000
Bar chart of market capital

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d)
From the analysis of returns of both the companies and its trends it is a better idea to invest in
TPM.
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526272829303132333435
-40%
-20%
0%
20%
40%
60%
80%
Trends for TLS and TPM
TLS Return TPM Return
Q2.
a. Mean of turnover for household goods : 4588.2
Standard deviation of turnover for household goods: 481.5941
Mean of turnover for clothing, footwear and personal accessory: 2089.783
Standard deviation of turnover for clothing, footwear and personal accessory: 427.70
Mean of turnover for Department stores: 1557.425
Standard deviation of turnover for Department stores: 424.15
Mean of turnover for other retailing: 3824.24
Standard deviation of turnover for other retailing: 468.79
Mean of turnover for Cafes, restaurants and takeaway food services: 3794.23
Standard deviation of turnover for Cafes, restaurants and takeaway food services:
222.43
b.
Household
goods
Clothing
etc
Department
stores
Other
retailing
Cafes etc
Min 4023.6 1632.2 1099.4 3334.5 3377.8

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Quartile 1 4360 1914.85 1401.725 3605.6 3676.125
Max 5826.5 3351.8 2813.5 5053.1 4278.9
Quartile 3 4689.675 2105.45 1540.4 3902.975 3913.5
c)
Household Goods Clothing etc Department
Stores Other Retailing Cafes etc.
0
1000
2000
3000
4000
5000
6000
7000
Box and Whisker Plots for each industry group
2(d)
Jan-18 Feb-18Mar-18 Apr-18May-18 Jun-18 Jul-18 Aug-18 Sep-18 Oct-18 Nov-18 Dec-18
0
1000
2000
3000
4000
5000
6000
7000
Trend for different indutry group
Household Goods Clothing etc Department Stores
Other Retailing Cafes etc.

7Statistic
Q3.
In thousands In thousands In thousands
In
thousands
In
thousands
Banking
Social
Networkin
g
Purchasing
goods Entertainment
Formal
Educational
Activities
Health
Services
Victoria 3469.7 3456.1 3129.4 3507.9 1374.3 2035.4
Queensland 2594.1 2584.4 2264.3 2487.2 1010.9 1461.9
South Aus 910.2 902.3 839.5 906.8 336.9 536
West Aus 1457.1 1451.6 1320.6 1433.9 505.7 863
Tasmania 271 274.3 263 274.2 87.9 153
Northern Territory 97.8 103.3 92.4 88.8 40.5 51.1
Aus Capital
Territory 249.8 227.3 242.7 256.7 85.7 162.7
a) P(Queensland) 0.2828
b) P(Social Networking/ Tasmania) 0.2073
c) P( Formal Educational Activities/Victoria) 0.0810
d) P( Banking) + P (Entertainment) 0.4105
Probability that a randomly selected household lives in Queensland: 0.2828
Probability that a randomly selected household lives in Tasmania and accesses the internet
for social networking purpose: 0.2073
Probability that a randomly selected household accesses the internet for formal educational
activities and lives in Victoria: 0.0810
Probability that a randomly selected household has accesses the internet for banking or
entertainment: 0.4105
Q4.
a)
Mean of the normally distributed bus arrival times: 51 minutes.

8Statistic
Std. Deviation of normally distributed bus arrival times: 4 minutes.
The value that the upper 5% of the time exceed has a z value 1.96.
That time is 1.96 Std. deviations above the mean: t = 51 + 1.96*4 = 58.84 mins.
b)
The height of year 3 students varies uniformly between 110 centimetres and 135 centimetres.
Probability that the height of year 3 student will be less than 121 centimetres
: ( 121−110 )
( 135−110 ) = 11
25 =0. 25
c)
If the participants have no ability to distinguish between the brands, then both the brands are
equally likely to be selected.
1)
Proportion of correct identification ( p0 ) : 50% = 0.5
Proportion of correct identification in the sample (p) = 65% =0.65
Z stat = (0.65−0.5)/ √ .5(1−.5)
250
= 0.15 / 0.0316
= 4.75
P( p > 0.65 ) = P( z > 4.75 )
= 0.0001 ( approx.)
2)
Probability that the sample will have between 60% and 70% of the identifications correct:
P ( 0.6 < p < 0.7)
= P ( 0.6−0.5
0.0316 < p < 0.7−0.5
0.0316 )=P(3.16< z< 6.33)
= .0117
Q5.
a)

9Statistic
Proportion of students who attend school in the district (P): 62%
290 students out of 500 students constitute (p): 290
500 ×100 %=58 %
Standard Deviation of the sampling distribution: σ = sqrt[ P * ( 1 - P ) / n ]
= √ .62(1−.62)
500 = 0.0217
Z statistic : .58−.62
.0217 = -1.84
P ( z ≥−1.84 )=¿ 1-.0329 = .9671
b)
p0=0.5 , p= 185
500 =0.37
σ = √ .5 (1−.5)
500 =0.0224
Let , H0 : p ≥ 0.5
Ha : p <0.5
z=(0.37−0.5)/¿0.0224
= -5.8
P value is much less than 0.05 so the null hypothesis can be rejected and it can be said that
there is significant evidence that the population proportion of travellers who select their
flights and cancel their bookings is less than 0.50.
c)
Mean of 210, 125, 80, 131, 105, 65, 84, 118, 95
= (210 +125 + 80 +131 + 105 +65 +84+118+95)/ 9
= 112.56
Standard Deviation : 42.61
Critical z value for 95% = 1.96
95 % CI for mean : 112.56 ± 1.96 42.61
√ 9 = 112.56 ± 27.832 = (84.728 ,140.392)

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References:
Black, K.U., 2019. Business statistics: for contemporary decision making. Wiley
Fry, G.S., 2019. Business statistics a decision-making approach. Pearson Education Limited.
Mayes, T.R., 2014. Financial analysis with microsoft excel. Nelson Education.
Pandey, I.M., 2015. Essentials of Financial Management, 4th Edtion. Vikas publishing
house.
Siegel, A., 2016. Practical business statistics. Academic Press.

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