A statistical study that was conducted to determine the feasibility of opening a Cell Phone Shop in PMU's Campus

1. Math
1313: Statistical Methods
Dr. Mohammed Al-Najjar
Fall 2012
Statistical Methods Course Project
Name: Ahmed Abdullah Aljabr
Section: 101
ID#: 201001926
Date: 29/12/2012
1

2. I-Introduction:
Introduction
Since the beginning of the new millennium, cellular phones are considered the new trend in technologies. Some
people consider them to be supplementary. On the other hand, with the rapid growth of globalization and the
world-wide operations within most corporations, it’s considered indispensable. In Saudi Arabia, many people
tend to buy the last cellular phone in market, just to stay up-to-date with technology. Generally, as it has been
observed, youth in Saudi Arabia are obsessed with cellular phones. Therefore, it’s an ideal opportunity to open a
cellular phones shop, if an accurate study was conducted for this matter.
Purpose of the Study
The aim of this research is to study the feasibility of opening a cellular phones shop in Prince Mohammed Bin
Fahad University. It will focus on many aspects including students’ purchasing desire, the type of cellular
phones mostly preferred, and the amount students are willing to pay. Collectively, these main aspects will
determine the possibility of opening the shop.
Methodology
Data collection
A questionnaire was distributed to a sample of students in PMU using “Systematic Sampling.” It’s a method of
selecting sample members from a larger population according to a random starting point and a fixed periodic
interval. In this case, 60 students was the target sample and the fixed interval was 5 students.
Questionnaire
Data will be collected by administering open-ended and close-ended questions for the sample. However, to
ensure that the study does not lose focus, structured questionnaire will be necessary. Questions asked will
include:
Which cellular phone brand do you prefer to use?
………………………………………
2

3. What is the most important feature you are looking forin a cellular phone?
………………………………………
What reputation do you have for Apple’s smartphones?
-Excellent
-Good
-Mediocre
-Bad
What reputation do you have for Samsung’s smartphones?
-Excellent
-Good
-Mediocre
-Bad
What reputation do you have for Nokia’s smartphones?
-Excellent
-Good
-Mediocre
-Bad
What reputation do you have for Blackberry’s smartphones?
-Excellent
-Good
-Mediocre
-Bad
How many cellular phones do you have?
-Zero
-One
-Two
-More (…….)
How many cellular phones have you bought last year?
-Zero
-One
-Two
-More (…….)
How many minutes do you spend using your cellphone every day?
………………………………
How much have you paid for your last cellular phone?
………………………………
Data analysis
After the data is collected, it will be displayed using all descriptive statistics tools, such as tables, graphs,
measures of center and variation, and relationship between different variables. Furthermore, all possible
inferential statistics tools will be presented, including estimations, testing of hypothesis, and finally a regression
model. Every outcome will be discussed and further analyzed in order to reach a conclusion.
3

4. II-Tables:
 [Nominal]Which cellphone brand do you prefer to use?
Row Labels
Frequency
Relative Frequency
Apple
20
33.33%
Blackberry
23
38.33%
Nokia
5
8.33%
Other
1
1.67%
Samsung
11
18.33%
Grand Total
60
100.00%
Comments:
71.6% of the people in this sample preferred Blackberry and Apple.Samsung is preferred by half as many as
people who prefer Blackberry.Less than 2% of the people in this sample use brands other than the ones
specified in this survey. This is a clear indication that the market is being controlled by these big four brands.
 [Ordinal]What kind of reputation do you have of Apple’s smartphones?
Relative
Cumulative
Relative Cumulative
Evaluation
Frequency
Frequency
Frequency
Frequency
Bad
1
1.67%
1
1.67%
Mediocre
3
5.00%
4
6.67%
Good
25
41.67%
29
48.33%
Excellent
31
51.67%
60
100.00%
Grand Total
60
100.00%
-
-
Comments:
The majority of the people in this sample have an excellent reputation for Apple’s smartphones. 6.67% of the
sample has a mediocre reputation for Apple’s smartphones or worse. Only 1 person had a bad reputation of
Apple’s smartphones. More than half the sample had an excellent reputation for Apple’s smartphones.
4

5.  [Discrete]How many cellular phones have you bought last year?
Relative
Cumulative
Relative Cumulative
Number
Frequency
Frequency
Frequency
Frequency
0
3
5.00%
3
5.00%
1
30
50.00%
33
55.00%
2
20
33.33%
53
88.33%
more
7
11.67%
60
100.00%
Grand Total
60
100.00%
Comments:
50% of the sample bought only 1 cellular phone last year. 33.33% of the sample bought 2 cellular phones last
year which is relatively high. Only 3 people in this sample never bought a cellular phone last year, which is low.
 [Continuous]How much have you paid for your last cellular phone?
Relative
Cumulative
Relative Cumulative
Range in S.R
Frequency
Frequency
Frequency
Frequency
0 - 500
5
8.33%
5
8.33%
500 - 1000
8
13.33%
13
21.67%
1000 - 1500
9
15.00%
22
36.67%
1500 - 2000
16
26.67%
38
63.33%
2000 - 2500
11
18.33%
49
81.67%
2500 - 3000
10
16.67%
59
98.33%
3000+
1
1.67%
60
100.00%
Grand Total
60
100.00%
Comments:
Only 1.67% of the sample bought a cellular phone for more than S.R 3000. Nearly one quarter of the sample, or
the majority of people in the sample, bought a cellular phone for a price between 1500 and 2000.There are 5
people in the sample who bought a cellular phone for S.R 500 or less. Students are willing to pay high prices.
5

6. III- Graphs:
 [Nominal]Which cellphone brand do you prefer to use?
Preferred Cellular Phone
18%
2%
Apple
34%
Blackberry
8%
Nokia
Other
Samsung
38%
Comments:
More than two thirds of the people in the sample preferred Apple’s and Blackberry’s smartphones. Only a small
proportion preferred other brands than the big four brands. Nokia is preferred by 8% of the sample, which
makes it the least favorable among the big four brands in the market.
 [Ordinal]What kind of reputation do you have of Apple’s smartphones?
Apple Reputation
35
31
30
25
25
20
Total
15
10
5
1
3
0
Bad
Medicore
Good
6
Excellent

7. Comments:
The majority of the sample has an excellent reputation of Apple’s smartphones. Only one person had a bad
reputation, which is nothing compared to the sample size. Also, only 4 people have a mediocre reputation or
less for Apple’s smartphones.
 [Discrete]How many cellular phones have you bought last year?
Number of Cellular Phones Bought
Last Year
7
3
0
1
2
20
30
more
Comment:
Half the people in the sample bought at least one cellular phone last year. Only 3 people did not buy any cellular
phones last year. One third of the sample bought two cellular phones last year. 50 student bought at least 1
cellular phones last year, which is a good sign for business.
7

8.  [Continuous]How much have you paid for your last cellular phone?
Frequency
Amount paid for last cellular phone
18
16
14
12
10
8
6
4
2
0
16
11
8
9
10
5
Frequency
1
250
750
1250
1750
2250
2750
More
S.R
Comments:
10 people bought a cellular phone for a value around S.R 2750. Only 1 person in the sample bought a cellular
phone for a value higher than S.R 2750. Most of the people in the sample bought a cellular phone for a value
around S.R 1750.
8

9. IV- Measures of Center:
 [Nominal] What is the most important feature you are looking for in a cellular phone?
Measure of center
Value
Mode
Applications
Comments:
The most frequent answer to this question was “Applications”. Thus, it is the Mode for this question.
Also, it is the preferred feature for the most of the people in the sample. Applications are important thus
this mode makes sense.
 [Ordinal] What kind of reputation do you have of Samsung’s smartphones?
Measure of center
Value
Mode
Good
Comments:
The most frequent answer to this question was “Good”. Thus, it is the Mode for this question.
Also, it is the dominant reputation to most of the people in the sample.Samsung’s smartphones should be
popular.
 [Discrete] How many cellular phones have you bought last year?
Measure of Centre
Arithmetic Mean
Geometric Mean
Median
Mode
Value
1.76666
1.55557
1.5
1
Comments:
The most frequent answer to this question was “1”. The middle value for the number of cellular phones
bought last year is equal to 1.5. The average number of cellular phones bought last year is 1.55 cellular
phones. The more accurate average is 1.76 cellular phones.
9

10.  [Continuous] How much have you paid for your last cellular phone?
Measure of Centre
Value
Geometric Mean
1501.24
Arithmetic Mean
1845.25
Median
1800
Mode
1800
Comments:
The most frequent answer to this question was S.R 1800. The middle number was also S.R 1800. The average
amount paid for last cellular phone is S.R 1845.25. The more accurate average amount is S.R 1501.24. Many
new cellular phones prices are around these measures, which is good for business.
10

11. V- Measures of Dispersion:
 [Discrete] How many cellular phones have you bought last year?
Measure of Variation
Value
Standard Deviation
0.9806
Sample Variance
0.9615
Range
4
Inter-Quartile Range
1
Co-efficient of Variation
55.50%
Comments:
The Arithmetic Mean to this question is (1.76). We calculated our Standard Deviation and it’s to equal
(±0.9806). The Range in the answer for this question is (4) which is the difference between the highest value
and the lowest. The Inter-Quartile Range is (1), which is the length between the second quarter and the third
quarter.
 [Continuous] How much have you paid for your last cellular phone?
Measure of Variation
Value
Standard Deviation
1054.52
Sample Variance
1112019.85
Range
7450
Inter-Quartile Range
1250
Co-efficient of Variation
102%
Comment:
The Arithmetic Mean to this question is (S.R 1845.25). We calculated our Standard Deviation and it’s to equal
(± 0.9806) The Range in the answer for this question is (7450) which is the difference between the highest value
and the lowest. The Inter-Quartile Range is (1250), which is the length between the second quarter and the third
quarter.
11

12. VI-Relationship between Two Variables:
 [Nominal] Contingency table showing the relationship between: Cellular phone brand (row),
Important feature (column)
Fast
Brand / Feature
4G
Applications
Grand
Camera Processor
Other
Total
Apple
50.00%
35.00%
0.00%
10.00%
5.00%
100.00%
Blackberry
13.04%
34.78%
4.35%
43.48%
4.35%
100.00%
Nokia
0.00%
0.00%
20.00%
80.00%
0.00%
100.00%
Other
0.00%
100.00%
0.00%
0.00%
0.00%
100.00%
Samsung
27.27%
45.45%
0.00%
27.27%
0.00%
100.00%
Grand Total
26.67%
35.00%
3.33%
31.67%
3.33%
100.00%
Comments:
50% of the people who preferred Apple’s smartphone chose the “4G” as their most important feature in a
cellular phone. 80% of the people who preferred Nokia’s smartphones chose the “Fast Processor” as their most
important feature, this means that Nokia’s smartphones have fast processors. 45.45% the people who preferred
Samsung’s smartphones chose the “Application” as their most important feature.
 [Ordinal] Contingency table showing the relationship between: Nokia’s reputation (row),
Blackberry’s reputation (column)
Nokia/Blackberry
Bad
Bad
Good
Excellent Medicore Poor
Grand Total
40.00%
0.00%
40.00%
0.00%
20.00%
100.00%
0.00%
11.11%
44.44%
44.44%
0.00%
100.00%
Excellent
14.29%
42.86%
14.29%
28.57%
0.00%
100.00%
Mediocre
5.00%
50.00%
20.00%
15.00%
10.00%
100.00%
Poor
0.00%
10.53%
10.53%
63.16%
15.79%
100.00%
Grand Total
6.67% 26.67%
21.67%
35.00% 10.00%
100.00%
Good
Comments:
40% of the sample who has a “Bad” reputation for Nokia’s smartphones also has a “Bad” reputation for
Blackberry’s smartphones. 20% of the sample who has a “Mediocre” reputation for Nokia’s smartphones has an
“Excellent” reputation for Blackberry’s smartphones.
12

13.  [Discrete] Contingency table showing the relationship between: Current cellular phones (row),
Number of cellular phones bought last year (column)
Current Cell/Bought Cell
0
1
2 More
Grand Total
One Cellular Phone
6.25%
53.13%
34.38%
6.25%
100.00%
Two Cellular Phones
3.57%
46.43%
32.14%
17.86%
100.00%
Grand Total
4.55% 48.86% 32.95% 13.64%
100.00%
Comments:
6.25% of the people who have one cellular phone never bought a cellular phone last year. 32.14% of the people
who have two cellular phones bought two cellular phones last year. This implies that people who have two
cellular phones are buying more than people who don’t, which means a big market for investors.
Correlation Co-Efficient:
Cell No.
Cell Bought
1
Cell No.
0.15458795
Cell Bought
1
Comments:
There is a weak positive relationship (15.45%) between the number of cellular phones bought last year by the
people in the sample and their current number of cellular phones.
 [Continuous] Correlation Co-Efficient:
Daily time (min)
Daily time (min)
SAR last cell
100.00%
-2.22%
SAR last cell
100.00%
Comments:
There is no relationship between the daily minutes spent on the cellular phones by the people in the sample and
the amount they have paid for their last cellular phone.
13

14. VII-Estimation:
 [Nominal] What feature you are looking for the most in a cellular phone? (Reply: Applications)
p
x
n
[p = percentage of successes | x
number of successes | n
sample size]
Given x= 21 | n= 60] Therefore, p = 0.35
Let
[p
z
/2
= 0.05, Therefore we have a (1-0.05= 95%) Confidence Interval
(1
n
)
, p
z
(1
/2
)
n
]
After applying the formula above we get the interval [33.44%-36.55%]
Comments:
We are 95% confident that the population’s proportion (π) that prefers“Applications” in cellular phones
is between [33.44%-36.55%]. This means that “Applications” are very important to most people.
 [Ordinal] What kind of reputation do you have for Samsung’s smartphones? (Reply: Good)
p
x
n
[p = percentage of successes | x
number of successes | n
sample size]
Given x= 29 | n= 60] Therefore, p = 0.4833
Let
[p
z
/2
= 0.05, Therefore we have a (1-0.05= 95%) Confidence Interval
(1
n
)
, p
z
(1
/2
)
n
]
After applying the formula above we get the interval [35.68%-60.97%]
Comments:
We are 95% confident that the population’s proportion (π) that has a “Good” reputation of Samsung’s
smartphones phones is between [35.68%-60.97%]. This implies an overall good reputation for Samsung.
14

15.  [Discrete]How many cellular phones have you bought last year?
Let
= 0.05 [Given
(
t
/2
S
n
,
t
= 1.58, S= 0.94, n= 60, Critical t= 2.04]
/2
S
n
)
After applying the formula above we get the interval [1.33 - 1.83]
Comments:
We are 95% confident that the population’s mean (µ) of the number of cellular phones bought last year
per person is between [1.33 - 1.83 cellular phones]. This infers that people are buying at least one
cellular phone per year, which is very good for business.
 [Continuous]How much have you paid for your last cellular phone?
Let
= 0.05 [Given
(
t
/2
S
n
,
t
=1845.45, S= 1054.52, n= 60, Critical t= 2.04]
/2
S
n
)
After applying the formula above we get the interval [1567.528 – 2122.973]
Comments:
We are 95% confident that the population’s mean (µ) of the amount paid for the last cellular phone is
between [S.R 1567.528 – S.R 2122.973]. This indicates that many people are willing to pay a high price
which falls with that range for a cellular phone.
15

16. VIII-Testing of Hypothesis:
 First: 1-Proportion z-test:
 [Nominal] What is the most important feature you are looking for in a cellular phone?
(35% of the sample replied “Applications”)
Null Hypothesis: the population’s proportion that prefers applications in cellular phones is equal to 55%.
-Down below is the null hypothesis (H0) and the alternative hypothesis (H1)
H0: π=0.55 , H1: π≠0.55
-To test our alternative hypothesis, we apply a 1-proportion z-test:
-Given
= 0.05 , P=0.35 , n=60
Z-Test:
-From the Z-Test above,Observed Z = -3.114
-Critical Values Z
/2=
± 1.96
Comments:
-Since the Observed Z is within the rejection region, we reject it.
-There is sufficient evidence to support our claim that the population’s proportion that prefers applications in
cellular phones is not equal to 55%.
 [Ordinal] What kind of reputation do you have of Samsung’s smartphones?
(48.33% of the sample replied “Good”)
Null Hypothesis: the population’s proportion that considers Samsung’s smartphones as “Good” is equal to
40%.
-Down below is the null hypothesis (H0) and the alternative hypothesis (H1)
H0: π=0.40, H1: π≠0.40
16

17. -To test our alternative hypothesis, we apply a 1-proportion z-test:
-Given
= 0.05 , P=0.4833 , n=60
Z-Test:
-From the Z-Test: Observed Z = -1.317
-Critical Values Z
/2=
± 1.96 (when
= 0.05)
Comments:
-Since the Observed Z is in not the rejection region, we don’t reject it.
-There is insufficient evidence to support our claim that the population’s proportion that considers Samsung’s
smartphones as “Good” is not equal to 40%.
 Second: 2-Proportion z-test:
 [Ordinal] What kind of reputation do you have for Samsung’s smartphones?
(48.33% of the sample replied “Good”)
 [Ordinal] What kind of reputation do you have forApple’s smartphones?
(41.66% of the sample replied “Good”)
Null Hypothesis: the population’s proportion that believes Samsung smartphones is “Good” is equal to the
population’s proportion that believes Apple’s smartphones is “Good.”
-Down below is the null hypothesis (H0) and the alternative hypothesis (H1)
H0: π1= π2, H1: π1≠π2
-To test our alternative hypothesis, we apply a 2-proportion z-test:
-Given
= 0.05, P1=0.4833 ,P2=0.4166 , n1=60, n2=60, D0= 0, Ṕ = 0.45
17

18. -From the Z-Test: Observed Z = 9.9075
-Critical Values Z
/2=
± 1.96 (when
= 0.05)
Comments:
-Since the Observed Z is within the rejection region, we reject it.
-There is sufficient evidence to support our claim that the population’s proportion that believes Samsung
smartphones is “Good” is not equal to the population’s proportion that believes Apple’s smartphones is “Good.”
 Third: 1-Sample t-test:
 [Discrete]How many cellular phones have you bought last year?
Null Hypothesis: the population’s mean for the number of cellular phones bought last year is equal to 2 cellular
phones.
-Down below is the null hypothesis (H0) and the researcher hypothesis (H1)
H0: µ=2, H1: µ ≠2
-To test our alternative hypothesis, we apply a 1-sample t-test:
-Given
= 0.05 ,
=1.76666, n=60, S= 0.9806, µ0= 2
t
X
S
0
n
-From the t-test above: Observed T = -1.8436
-Critical Values T /2= ± 2.04 (when
= 0.05)
Comments:
-Since the Observed T is in not the rejection region, we don’t reject it.
18

19. -There is insufficient evidence to support our claim that the population’s mean for the number of cellular
phones bought last year is not equal to 2 cellular phones.
 Fourth: 2-Sample t-test:
 [Nominal] Which cellphone brand do you prefer to use?
(20 replied “Apple”, 23 replied “Blackberry”)
 [Continuous]How much have you paid for your last cellular phone?
1:
the mean for the people who replied “Apple” = 1926.5
2:
the mean for the people who replied “Blackberry” = 1951.52
Null Hypothesis:the average amount paid for last cellular phone by people who prefer “Apple” is equal to the
average amount paid for last cellular phone by people who prefer “Blackberry.”
-Down below is the null hypothesis (H0) and the researcher hypothesis (H1)
H0: µ1=µ2, H1:µ1≠µ2
-To test our alternative hypothesis, we apply a 2-sample t-test:
-Given
= 0.05 ,
1=1926.5,
2= 1951.52,
n1=20, n2=23,S1= 832.58, ,S2= 1316.79
X1 X 2
t
2
S12 S 2
n1
n2
-From the t-test above: Observed T = -0.07541
-Critical Values T /2= ± 2.04 (when
= 0.05)
Comments:
-Since the Observed T is in not the rejection region, we don’t reject it.
-There is insufficient evidence to support our claim that the average amount paid for last cellular phone by
people who prefer “Apple” is not equal to the average amount paid for last cellular phone by people who prefer
“Blackberry.”
19

20.  Fifth: One-Way ANOVA:
 [Nominal] Which cellphone brand do you prefer to use?
(20 replied “Apple”, 23 replied “Blackberry”, 5 replied “Nokia”)
 [Continuous] How many minutes do you spend using your cellphone every day?
1:
the mean for the people who replied “Apple” = 198.75
2:
the mean for the people who replied “Blackberry” = 266.087
3:
the mean for the people who replied “Nokia” = 168
Null Hypothesis:the average minutes spent on cellular phones by people who prefer “Apple”, “Blackberry”,
and “Nokia” are equal.
-Down below is the null hypothesis (H0) and the researcher hypothesis (H1)
H0: µ1=µ2=µ3, H1:the average minutes spent on cellular phones by people who prefer “Apple”,
“Blackberry”, and “Nokia” are not equal.
-To test our alternative hypothesis, we apply a one-way ANOVA test:
SST
F
SSE
K 1
n K
-From the t-test above: Observed F = 0.5935
-Critical Values F= 3.2043 (when
= 0.05)
Comments:
-Since the Observed F is in not the rejection region, we don’t reject it.
-There is insufficient evidence to support our claim that the average minutes spent on cellular phones by people
who prefer “Apple”, “Blackberry”, and “Nokia” are not equal.
20

21. IX- Regression:
From the survey’s data, 1 dependent data was chosen and 2 independent as well:
 Dependent:How many minutes do you spend using your cellphone every day? [Continuous]
 Independent: - How many cellular phones have you bought last year? [Discrete]
- How many cellular phones do youhave? [Discrete]
From these questions, the following things can be obtained:
 R Square= 0.6619
 A Regression Model:
Daily minutes=
796.94*(Current number of cellular phones) + 323.01*(Cellular phones bought last year) + e
Comment:
66.19% of variability in “Daily minutes” is explained by “Current number of cellular phones” and
“Cellular phones bought last year”.
21

22. X- Conclusion:
To conclude, the research’s outcomes met the expectations. Clearly, cellular phones businesses yield high
returns, especially in Saudi Arabia. Most of the students in PMU are willing to buy cellular phones every
year for a relatively high price. Many results indicate that students’ purchasing desire is high; they most
likely would be dependable customers for this shop. The shop must have sufficient supplies of the big four
cellular phones brands in order to satisfy the demand, yet in different quantities. In short, opening a cellular
phones shop in PMU would be a great investment.
22