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

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

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

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

  • 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
  • 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 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
  • 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
  •  [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
  • 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
  • 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
  •  [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
  • 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
  •  [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
  • 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
  • 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
  •  [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
  • 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
  •  [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
  • 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
  • -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
  • -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
  • -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
  •  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
  • 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
  • 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