Feasibility Study: Opening a Cell Phone Shop in PMU's Campus

Math

1313: Statistical Methods

Dr. Mohammed Al-Najjar

Fall 2012

Statistical Methods Course Project

1

Name: Ahmed Abdullah Aljabr ID#: 201001926Section: 101 Date: 29/12/2012

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

What is the most important feature you are looking for in 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?


What reputation do you have for Nokia’s smartphones?


What reputation do you have for Blackberry’s smartphones?


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.

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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?

Evaluation

Frequenc

y

Relative

Frequency

Cumulative

Frequency

Relative Cumulative

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.

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[Discrete] How many cellular phones have you bought last year?

Number Frequency

Relative

Frequency

Cumulative

Frequency

Relative Cumulative

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%


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?

Range in S.R Frequency

Relative

Frequency

Cumulative

Frequency

Relative Cumulative

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%


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.

III- Graphs: 5

[Nominal] Which cellphone brand do you prefer to use?

33%

38%

8%

2%

18%

Preferred Cellular Phone

AppleBlackberryNokiaOtherSamsung

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?

Bad Medicore Good Excellent0

5

10

15

20

25

30

35

13

25

31

Apple Reputation

Total

Comments:

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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.


3

3020

7

Number of Cellular Phones Bought Last Year

012more

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.

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250 750 1250 1750 2250 2750 More02468

1012141618

5

8 9

16

11 10

1

Amount paid for last cellular phone

Frequency

S.R

Freq

uenc

y

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.

IV- Measures of Center: 8

[Nominal] What is the most important feature you are looking for in a cellular phone?

Measure of center Value

Mode

Application

s

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.


Measure of Centre ValueArithmetic Mean 1.76666Geometric Mean 1.55557Median 1.5Mode 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

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.

V- Measures of Dispersion: 10


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.


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.

VI-Relationship between Two Variables: 11

[Nominal] Contingency table showing the relationship between: Cellular phone brand (row),

Important feature (column)

Brand / Feature 4G Applications Camera

Fast

Processor Other

Grand

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 Good

Excellen

t

Medicor

e Poor

Grand

Total

Bad 40.00% 0.00% 40.00% 0.00% 20.00% 100.00%

Good 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%

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.

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[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

Cell No. 1

Cell Bought 0.15458795 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) SAR last cell

Daily time (min) 100.00%

SAR last cell -2.22% 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.

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VII-Estimation: [Nominal] What feature you are looking for the most in a cellular phone? (Reply: Applications)

p= xn [p = percentage of successes | x number of successes | n sample size]

Given x= 21 | n= 60] Therefore, p = 0.35

Let = 0.05, Therefore we have a (1-0.05= 95%) Confidence Interval

[

p−zα /2 √ π (1−π )n

,

p+zα /2√ π (1−π )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= xn [p = percentage of successes | x number of successes | n sample size]

Given x= 29 | n= 60] Therefore, p = 0.4833

Let = 0.05, Therefore we have a (1-0.05= 95%) Confidence Interval

[

p−zα /2 √ π (1−π )n

,

p+zα /2√ π (1−π )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.

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Let = 0.05 [Given xP = 1.58, S= 0.94, n= 60, Critical t= 2.04]

(μ− tα /2

S

√n ,μ+tα /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.


Let = 0.05 [Given xP = 1845.45, S= 1054.52, n= 60, Critical t= 2.04]

(μ− tα /2

S

√n ,μ+tα /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.

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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:

(P−π0)

√ π0(1−π0)N

-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)16

H0: π=0.40, H1: π≠0.40


-Given = 0.05 , P= 0.4833 , n= 60

Z-Test:

(P−π0)

√ π0(1−π0)N

-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?


[Ordinal] What kind of reputation do you have for Apple’s smartphones?


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


-Given = 0.05, P1= 0.4833 , P2= 0.4166 , n1= 60 , n2= 60, D0= 0, Ṕ= 0.45

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2−Proportion Z test=(P1−P2 )−D0

√ ṕ(1−ṕ)n1

+ṕ (1−ṕ)n2

-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:


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 , xP = 1.76666, n= 60, S= 0.9806, µ0= 2

t=X̄−μ0

S√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.

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-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:


(20 replied “Apple”, 23 replied “Blackberry”)


xP 1: the mean for the people who replied “Apple” = 1926.5

xP 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.”


H0: µ1= µ2, H1: µ1≠ µ2

-To test our alternative hypothesis, we apply a 2-sample t-test:

-Given = 0.05 , xP 1= 1926.5, xP 2= 1951.52, n1= 20, n2= 23, S1= 832.58, , S2= 1316.79

t=X̄1− X̄2

√ S12

n1

+S2

2

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.”

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Fifth: One-Way ANOVA:


(20 replied “Apple”, 23 replied “Blackberry”, 5 replied “Nokia”)

[Continuous] How many minutes do you spend using your cellphone every day?

xP 1: the mean for the people who replied “Apple” = 198.75

xP 2: the mean for the people who replied “Blackberry” = 266.087

xP 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.


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:

F=

SSTK−1

SSEn−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.

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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 you have? [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”.

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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.

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Feasibility Study: Opening a Cell Phone Shop in PMU's Campus

Economy & Finance

Transcript of Feasibility Study: Opening a Cell Phone Shop in PMU's Campus