Insight into Market Share and Usage of Mobile Phones by Students at La Trobe University

This document provides an insight into the market share and usage of mobile phones by students at La Trobe University. It includes information on the proportion of female and male students, iPhone and Samsung Galaxy users, and average monthly earnings. Additionally, it analyzes the effect of price on preference between Samsung and Apple smartphones.

Cover Page
Research Project-2: BUS1BAN
Teacher’s Name
Workshop Details
(Time, day, room)
Students ID Number Students Name Student contribution*
(%)
e.g. 50% means the
student will receive 50%
of the marks awarded
Students Signature
*All group members are to exert an equal amount of effort on all questions of the assignment.
Students should not divide sections. If a student has contributed to only some sections, the
contribution of the student should be equal to the marks it carries. A student with less than
100% contribution will receive marks proportional to their contribution.
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An insight into market share and usage of
mobile phones by students at La Trobe University
Note: Students would continue to be the part of the same group as were
for research project-1 and would be utilising the data from the same
random sample that they have already submitted earlier.
Inferential Statistics
1. Point Estimate and Confidence Interval: (20 marks)
A. Suppose you randomly select a student from BUS1BAN class, how likely
is it that the student selected will be: (5 marks)
 A female;
 A male;
 An IPhone user;
 A Samsung Galaxy user.
Proportion ( ^p)
Female Students 0.52
Male Students 0.48
IPhone Users 0.69
Other Smart Phone Users 0.1
B. Estimate 95% confidence interval of the proportion of female students and the
proportion of Other Smart Phone User. Show the confidence intervals
graphically, and interpret your results. (You must show the formula and show
working by putting values in the formula accordingly): (5 marks)
i.Female Students (2.5 marks)
Lower limit = 0.44
Upper limit = 0.60
This results show that 95% of the times the proportion of females will always
be between 0.44 and 0.60
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ii.Other Smart Phone Users (2.5 marks)
Lower limit = 0.05
Upper limit = 0.15
This results show that 95% of the times the proportion of those who use
other smartphones will always be between 0.05 and 0.15
Proportion of females Proportion of other smartphone users
0
0.1
0.2
0.3
0.4
0.5
0.6
95% C.I for proportion
Figure 1
C. What are the average monthly earnings of male and female students at
La Trobe? (5 mark)
Female Male
Average Monthly
Earnings ($)
1162.46 1286.83
D. Provide 95% confidence interval of the average monthly earnings for each
gender, show the confidence intervals graphically, and interpret your answer.
(5 marks)
i.Female (2.5 marks)
Lower limit 976.96
Upper limit 1365.16
ii.Male. (2.5 marks)
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Lower limit 1043.17
Upper limit 1527.29
2. Hypothesis Testing: (20 marks)
A US market survey shows that the market share of iPhone is more than 40% of the US
market. Is it true for La Trobe students as well? Use your sample data to test this claim at
5% level of significance and interpret your answer. (Clearly label and follow the 5 steps of
hypothesis testing procedure as outlined on the formula sheet and you must show the
formula and show working by putting values in the formula accordingly).
hypothesized proportion 0.4
n 150
Proportion of Iphone users 0.69
Step 1
H0: Market share of Iphone > 40%
H1: Market share of Iphone <= 40%
Step 2
Alpha 0.05
Step 3
Proportion calculated 0.69
Standard error 0.04
Test statistics Z 7.25
Step 4
P-value one tail to right 2.08389E-13
Step 4
Critical value one tail to right
1.64485362
7
Step 5
Decision and conclusion
Because the p-value of 0.00 is less than the value of alpha 0.05, we reject the null
hypothesis and accept the alternative
There is a strong statistical evidence to support the claim that market share of Iphone is
more than 40% of market in US
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3. The effect of price on preference [Samsung versus Apple]: (50 marks)
A. IPhone and Samsung are two important players in the smartphone market
who compete against each other. Samsung’s phones are generally sold
cheaper than Apple’s smartphones. Complete the following table using the
survey data responses (5 marks)
Discount offered
on Samsung
Galaxy
Proportion of students who said they would buy the
latest Samsung Galaxy instead of the latest iPhone if
the price of Samsung Galaxy were discounted.
x Y(f) Y(m)
0% 0.107 0.167
5% 0.107 0.187
10% 0.107 0.187
15% 0.12 0.173
20% 0.16 0.207
25% 0.16 0.247
30% 0.187 0.287
35% 0.207 0.287
40% 0.253 0.327
45% 0.293 0.347
50% 0.293 0.380
B. Produce an appropriate graph to explain the relationship between discount
offered by Samsung on its latest Galaxy vis-à-vis the latest iPhone and change in
potential market share of Samsung Galaxy by using data in part 3-A. (5 marks)
0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
Scatterplot of discount offered and
proportion of female students
Discount offered on samsung galaxy
Proportion of female students
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0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
0.400
Scatterplot of discount offered and
proportion of male students
Discount offered on samsung galaxy
proportion of male students
C. Using excel provide the following statistical measures to explain the
relationship between discount offered by Samsung on its latest Galaxy vis-à-vis
the latest iPhone and change in potential market share of Samsung Galaxy by
using data in part 3-A. (5 marks)
Female Male
Covariance 0.0116
0.00534
1
Coefficient of Correlation
0.96689
1
0.96860
9
Coefficient of
Determination
0.93487
7
0.93820
4
Y-intercept
0.07575
8
0.14333
3
Slope
0.42181
8
0.44242
4
Least Squares Line
Graph showing least square line for males
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0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.000
0.100
0.200
0.300
0.400
Scatterplot of discount offered and proportion of
male students
Discount offered on samsung galaxy
proportion of male students
Graph showing least square line for females
0.00 0.10 0.20 0.30 0.40 0.50 0.60
0.000
0.050
0.100
0.150
0.200
0.250
0.300
0.350
Scatterplot of discount offered and proportion
of female students
Discount offered on samsung galaxy
Proportion of female students
D. Using data in part (3-A), perform linear regression using excel and follow the
instructions below: (35 marks)
i. Paste the excel output of linear regression hereunder. (3 marks)
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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.966891
R Square 0.934877
Adjusted R Square 0.927641
Standard Error 0.019461
Observations 11
ANOVA
df SS MS F Significance F
Regression 1 0.048931 0.048931 129.2006 1.22035E-06
Residual 9 0.003408 0.000379
Total 10 0.052339
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.075758 0.010977 6.901269 7.06E-05 0.050925108 0.100590044
x (discount offered) 0.421818 0.03711 11.36664 1.22E-06 0.337869118 0.505767245
ii. What type of linear regression is it and why? (3 marks)
(Hint: Simple or Multiple)
It’s a simple linear regression since there is only one independent variable.
iii. Report the values of slope coefficient and intercept? (4 marks)
Slope Coefficient: 0.42
Intercept: 0.076
iv. Using information from (i) or (iii) above write down the linear regression
equation. (Note similarity between linear regression equation with the
least square line in 3-C). (3 marks)
proportionof females=0.42 ( discount offered ) +0.076
v. Interpret Intercept: (3 marks)
The intercept (0.076) means that if the discount will not be offered (0%
discount), the proportion of females who will go for Samsung smartphones is
0.076.
vi. Interpret Slope Coefficient: (3 marks)
The slope coefficient (0.42) means that a unit change in discount offered causes
a 0.42 change in proportion of female students who buy Samsung phone.
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vii. Interpret Coefficient of determination: (3 marks)
The coefficient of determination (R-squared = 0.93) indicates that 93% of the
variation that occurs in the proportion of female students is explained by the
amount of discount offered.
viii. What is the relationship between Coefficient of Correlation and Coefficient
of Determination? Compute Coefficient of Correlation by using Coefficient
of Determination (Show working): (3 marks)
The coefficient of determination is the square of coefficient of correlation.
Correlation coefficient = 0.966891
Coefficient of determination = 0.934877
0.9668912=0.934878 Hence proved
ix. Perform hypothesis testing to test slope for linear relationship by using t-
statistics in the excel output. (Clearly label and follow the 5 steps of
hypothesis testing procedure as outlined on the formula sheet and you
must show the formula and show working by putting values in the formula
accordingly). (10 marks)
Step 1
H0: β =0
H1: β ≠ 0
Step 2
Alpha 0.05
Step 3
Test statistics t 11.667
Step 4
P-value one tail to right 0.00
Step 4
Because the p-value of 0.00 is less than the value of alpha 0.05, we reject the null
hypothesis and accept the alternative
There is a strong statistical evidence to support the claim that β is not equal to zero.
4. Summary and discussion (10 marks):
Provide a summary of the above analysis by covering the following points:
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 Compare the confidence interval estimates of part 1-B and 1-D in terms of conditions used
to employ specific formulae. Why does part 1-B differ from 1-D (conceptually not
numbers)? (4 to 6 lines – 3 marks)
There is a great difference between the two parts. This is because one is confidence interval for
proportion while the other one is confidence interval for the mean. The mean refers to a
measure of centre and takes into account the entire sample while proportion only takes into
account the points of interest. That is why the two intervals are different and hence using
different formulas.
 Summarise the hypothesis testing in part 2 (conceptually not numbers) by explaining the
conditions used to employ specific formula. (4 to 6 lines – 3 marks)
Because the p-value of 0.00 is less than the value of alpha 0.05, we reject the null hypothesis and
accept the alternative
There is a strong statistical evidence to support the claim that market share of Iphone is more
than 40% of market in US.
 Summarise regression analysis starting with differentiating between simple and multiple
regression, discussing relationship between the two variables by explaining intercept,
slope and R square. (10 to 12 lines – 4 marks)
There is a difference in simple linear regression and multiple linear regression. Multiple linear
regression is a regression that involves more than one independent variable. Simple linear
regression on the other hand involves only one independent variable. The coefficient of
determination (R-squared = 0.93) indicates that 93% of the variation that occurs in the
proportion of female students is explained by the amount of discount offered. The
intercept (0.076) means that if the discount will not be offered (0% discount), the
proportion of females who will go for Samsung smartphones is 0.076. The slope
coefficient (0.42) means that a unit change in discount offered causes a 0.42 change in
proportion of female students who buy Samsung phone.
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Please use Harvard Style of Referencing
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