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1. A. What proportion of the students in your sample are male and what proportion are female? Report your results in the following table. 
Gender Sample proportion
Female
Male

B. Use an appropriate chart to graphically display information in the table above.

C. Explanation.

2. Average Monthly Bill:

A. What is the average monthly bill of students by gender in your sample? Report your results in the following table.

Female Male
Average Monthly Bill ($)
B. Use an appropriate chart to graphically display information in the table above
C. Compare the average monthly bill of females and males.

3. Earnings and money spent on mobile phone:
A. What is the average monthly earning of students by gender in your sample? Report your results in the following table. 
Female Male
Average Monthly Earnings ($)
B. Is there any relationship between earning and money spent on mobile usage? Use an appropriate chart to illustrate your answer.
C. Provide the following statistical measures to test the relationship between earning and money spent on mobile usage.
D. What do the statistics in part [C] tell you about the relationship between earning and money spent on mobile usage for males and females? Explain your results. 

Gender Proportion

According to the current market scenario, Apple and Samsung are two established companies. Apple is a company that balances performance and efficiency. Apple is an incredibly successful product. Samsung is a less popular mobile company that is trying to provide similar features in mobile phones in lesser price. The mobile phones of Samsung are therefore getting popular day by day. They are also planning to set discount on prices of mobiles and increase their sale.

The current study collects the samples of 679 samples among which randomly selected 200 samples are considered for analysis. The survey technique is utilised for data collection.

Both qualitative and quantitative data are analysed with the undertaken research design. The data is analysed in MS-Excel software. This exploratory study design discovers the hidden facts regarding preference of Apple or Samsung mobiles (Chang, Kim and Joo 2013).

Gender Proportion:

What proportion of the students in your sample are male and what proportion are female? Report your results in the following table. 

Gender

Sample proportion

Female

0.4686

Male

0.5314

Use an appropriate chart to graphically display information in the table above.

The total number of surveyed samples is 175. The number of females is 82 and the number of males is 93. The proportion of females and males is 47:53 (approx.).

What is the average monthly bill of students by gender in your sample? Report your results in the following table. 

Female

Male

Average Monthly Bill ($)

$75.47

$68.17

Use an appropriate chart to graphically display information in the table above.

Compare the average monthly bill of females and males. 

The average monthly bill for phone usage of females is $75.47. The average monthly bill for phone usage of males is $68.17. It indicates that average monthly bill is greater for females than males. Hence, most of females spend more money than males in case of phone usage in a month.

Earnings and money spent on mobile phone:

What is the average monthly earning of students by gender in your sample? Report your results in the following table.

The Pearson correlation coefficient between two numerical variables “Earning Amount” and “Monthly phone usage bill” is 0.0203. Hence, these two variables are uncorrelated.

The value of multiple R-square assuming “Earning Amount” as independent variable and “Monthly phone usage bill” as dependent variable is found to be 0.0004. This refers the absence of linear association between dependent and independent variables. 

Female

Male

Covariance

-3122.08

-561.018

Coefficient of Correlation

0.0363

0.0097

Coefficient of Determination

0.0013

0.0001

Y-intercept

78.7461

69.0833

Slope

-0.0024

-0.0008

Least Squares Line

Mobile bill (Y) = 78.7461 -0.0024 * Earning amount (X)

Mobile bill (Y) = 69.0833 -0.0008 * Earning amount (X)

The coefficient of correlation and coefficient of determination between two variables “earning” and “money spent on mobile usage” is calculated for both the genders that are females and males.

Earnings and money spent on mobile phone

The correlation and coefficient of determination are greater for the linear model of females than the males. Hence, the association and link between these two factors are higher in case of females than males. The higher value of “slope” for linear model of females is greater than the value of “slope” for linear model of males. Therefore, the relevance of dependent and independent variable is greater for the regression model of females. The negative slopes refer the negative relevance between dependent and independent variables.

Market share of mobile phone brand

Complete the following cross classification tables  

Cross classification table by frequency 

Brand

Total

Apple

Samsung

LG

Do not use mobile phone

Other smart phone

Basic mobile phone

Gender

Male

62

19

2

0

10

0

93

Female

66

10

1

0

5

0

82

Total

128

29

3

0

15

0

175

Cross classification table by total relative frequency

Brand

Total

Apple

Samsung

LG

Do not use mobile phone

Other smart phone

Basic mobile phone

Gender

Male

0.354

0.109

0.011

0.000

0.029

0.000

0.503

Female

0.377

0.057

0.006

0.000

0.057

0.000

0.497

Total

0.731

0.166

0.017

0.000

0.086

0.000

1.000

Use an appropriate chart to graphically display the information above.

Is there any difference in the market share of each mobile phone brand by gender?

The use of Apple mobile is maximum (128) among the surveyed students. Females use Apple mobiles (66) more than Males (62). Very insignificant number of students use basic mobile phones or LG mobile phones. Similarly, the number of students who use basic mobile phones are very insignificant in frequency.  The habit of using Samsung mobile phone is greater in males (19) than females (10). Therefore, females generally prefer to use Apple mobile phones whereas males keep their faith in Apple mobiles as well as in Samsung and other smartphones.

Relationship between the earning of students and choice of mobile phone

Calculate the average income of students by brand. Report your results in the following tables 

Frequency

Brand

Total

Apple

Samsung

LG

Do not use mobile phone

Other smart phone

Basic mobile phone

Average income ($)

1347.09

1315.13

1533.33

00

808.33

00

1299.10

Use an appropriate chart to graphically display the information above and summarise the results.  

The bar chart displays that highest average earning of the students who uses LG mobiles ($1533.33) followed by the students who uses Apple mobiles ($1347.49). The students whose earnings are lower than $1000 on an average uses other smartphones. However, the students who prefer Samsung mobile phones has average monthly earning $1315.13.

Divide income into three categories at your discretion (low, middle and high) and complete the following tables.

The income level is divided in three categories that are Low, Middle and high. The income less than $2000 is “Low”, the income more than $2000 and less than $4000 is “Middle” and the income more than $4000 is considered “High” (Samuels, Witmer and Schaffner 2012). 

Cross classification table by frequency

Brand

Total

Apple

Samsung

LG

Do not use mobile phone

Other smart phone

Basic mobile phone

Income Level ($)

High  

3

0

0

0

0

0

3

Medium

29

9

1

0

1

0

40

Low

96

20

2

1

14

0

132

Total

128

29

3

1

15

0

175

 Cross classification table by total relative frequency

Brand

Total

Apple

Samsung

LG

Do not use mobile phone

Other smart phone

Basic mobile phone

Income Level ($)

High  

0.017

0.000

0.000

0.000

0.000

0.000

0.017

Medium

0.166

0.051

0.006

0.000

0.006

0.000

0.229

Low

0.549

0.114

0.011

0.000

0.080

0.000

0.754

Total

0.731

0.166

0.017

0.000

0.086

0.000

1.000

Employ an appropriate graph to compare the distribution of brand selection across the income groups. 

Market share of mobile phone brand

Provide an explanation on relationship between income and the choice of mobile phone. Is there a relationship?

The bar chart indicates that students of all levels of income prefer “Apple” mobiles whereas students of low level income especially like to use “Apple” mobiles. High income level students only use Apple mobiles. Use of Samsung molies is also significant for the students who are in the lower income category. LG mobile and other smartphone users are only in the medium and lower income level. The use of other smartphones is also higher in low level income category.

The effect of price on preference [Samsung versus Apple]

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  

Discount offered on Samsung Galaxy

Proportion of customers who said they will buy the latest Samsung Galaxy instead of the latest iPhone if the Galaxy was discounted.

x

y

0%

0.2343

5%

0.2457

10%

0.2686

15%

0.2514

20%

0.3200

25%

0.3543

30%

0.4171

35%

0.4229

40%

0.5086

45%

0.5314

50%

0.5886

(Miranda et al. 2014)

Using Excel, produce a scatter plot to summarize the relationship between potential market share and proposed discount offered by Samsung on its latest Galaxy vis-à-vis the latest iPhone.

The correlation between proportion of customers as market share and discount offered is positive and very high.

Complete the following table then interpret the statistics. 

Statistic

Covariance

0.1852

Coefficient of Correlation

0.975662

Coefficient of Determination

0.9519

Y-intercept

0.1914

Slope

0.7408

Least Squares Line

Proportion of Customers as market share = 0.1914 + 0.7408*Discount Offered

Using your answer to [A], [B] and [C], does Samsung’s market share, relative to Apple, increase or decrease with the discount offered by Samsung? Which customers are more loyal to their brand?

As the rate of discount increases, the possibility of buying Samsung mobiles rather than Apple mobiles increase. A high correlation and a greater value of coefficient of determination provide the evidence of that fact.

It could be interpreted that the number of customers of Apple mobiles decrease as the discount rate of Samsung mobile increases. Therefore, the customers of Apple mobiles are found to be less loyal rather than customers of Samsung mobiles.

The effect of price on preference & gender[Samsung versus Apple]: 

Compare the discount and market-share relationship in question 6 across gender.

Complete the following table using the survey data responses 

Discount offered on Samsung Galaxy

Proportion of customers who said they will buy the latest Samsung Galaxy instead of the latest iPhone if the Galaxy was discounted

Females

Males

x

yF

yM

0%

0.1585

0.3011

5%

0.2439

0.2473

10%

0.2439

0.2903

15%

0.2317

0.2689

20%

0.2805

0.3549

25%

0.3171

0.3871

30%

0.3537

0.4731

35%

0.3659

0.4731

40%

0.4390

0.5699

45%

0.4634

0.5914

50%

0.5244

0.6452

Using Excel, produce a scatter plot to summarize the relationship between potential market share of males and females, and proposed discount offered by Samsung on its latest Galaxy vis-à-vis the latest iPhone.

The correlation between proportion of market share for females and discount offered is higher for males than females. Therefore, the tendency to adopt Samsung mobiles rather than iPhone is high for males than females.

Complete the following table and note any differences between the statistics for females and males. 

Statistic

Females

Males

Covariance

0.01652

0.02028

Coefficient of Correlation

0.97688

0.95832

Coefficient of Determination

0.9543

0.9184

Y-intercept

0.1641

0.2156

Slope

0.6608

0.8113

Least Squares Line

Proportion of Customers as market share = 0.1641 + 0.6608*Discount Offered

Proportion of Customers as market share = 0.2156 + 0.8113*Discount Offered

Relationship between the earning of students and choice of mobile phone

(Chatterjee and Hadi 2006)

Using your answer to [A], [B] and [C], does Samsung’s market share, relative to Apple, increase or decrease across gender, with the discount offered by Samsung? Is there a difference in brand loyalty for females and males?  (1 mark)

The market share of Samsung relative to Apple increases across gender according to the increment in the rate of discount.

The trend lines or least square lines refer that females are more loyal towards iPhone rather than males. With same amount of discount in the price of Samsung mobiles, females are less eager to shift towards Samsung brand from Apple than males.  

Suppose, you randomly selected a student from the 2017 BUS1BAN class.

How likely is it that the student will be a female and how likely is it that the student will be a male? 

Female

Male

Sample proportion ()

0.5096

0.4904

Provide 95% interval estimates for each gender, show the confidence intervals graphically, and interpret your results.

The 95% interval estimates of proportions of females are 0.5471 (upper confidence interval) and 0.4720 (lower confidence interval). The 95% interval estimates of proportions of males are 0.5280 (upper confidence interval) and 0.4528 (lower confidence interval).

Females 

(Newcombe 1998)

How likely is it that the student will be using a smartphone? Provide a 99% interval estimate, show the confidence interval graphically and interpret your results. (3 marks) 

Smart phone users

Sample proportion

0.9956

The sample proportion is 0.9956. The 99% interval estimates of a randomly selected student using a smartphone are 1.0021 (upper interval estimate) and 0.9890 (lower interval estimate).

Confidence intervals (part 2): (8 marks)

What is the average monthly earnings of male and female students at La Trobe?   

Female

Male

Average Monthly Earnings ($)

$1260.912

$1230.527

Provide 95% interval estimates for each gender, show the confidence intervals graphically, and interpret your answer. 

The 95% confidence interval estimates for average monthly earnings of females are $1369.406 (Upper confidence limit) and $1152.418 (Lower confidence limit). The 95% confidence interval estimates for average monthly earnings of males are $1334.84 (upper confidence limit) and $1126.214 (Upper confidence limit). 

A US market survey shows that the market share of iPhone is more than 40% of the US market. Is this true for La Trobe students as well? Use your sample data to test this claim at 1%, 5% and 10% levels of significance and interpret your answers.

Hypotheses:

Null hypothesis: The market share of iPhone is more than 40% of the US market.

Alternative hypothesis: The market share of iPhone is less than or equal to 40% of the US market.

The effect of price on preference [Samsung versus Apple]

Observations:

The total number of mobile users = 679.

The total number of Apple mobile users = 521.

The proportion of Apple mobile users = 0.754.

Test applied:

One sample proportional z-test.

Outcomes:

The calculated z-statistic = 18.83.

The calculated significant p-value = 1.

The three-critical p-values are 0.01, 0.05 and 0.1.

Inference:

As per one-sample proportional z-test,

At 1% level of significance, we can accept the null hypothesis (Koch 2013).

At 5% level of significance, we can accept the null hypothesis.

Also, at 10% level of significance, we can accept the null hypothesis.

Therefore, according to all three types of levels of significance (1%, 5% and 10%), the null hypothesis is accepted. Therefore, it is more than 99% evident that the market share of Apple mobiles (iPhone) is greater than 40% of the US market.

The summarization of whole analysis refers that the Apple is very popular brand in the market. People of any socio-economic condition prefer to use iPhone than any other brand. Females prefer iPhone than males. The analysis of data of La Trobe students display that the preference of iPhone is also satisfying the real market scenario. Here, the people of lower economic class like to use Apple mobiles more than middle level or high-level classes. Females are also preferring Apple mobiles than males of La Trobe students. Besides, the students of La Trobe, especially the male students are willing to shift their usage from iPhone to Samsung mobiles.

The data on which analysis was carried out, was gathered by survey questionnaire method. The survey questionnaire had limited number of questions. Addition of more questions in the questionnaire may enhance the depth of the research investigating the more hidden reasons of the tendency of shift from iPhone to Galaxy mobiles.

As the randomisation technique is applied, the analysis is not hugely affected by bias. The analysis of data of La Trobe students more or less supports the market share of iPhones and other phones as Australian market. 

Reference List 

Bland, M., 2015. An introduction to medical statistics. Oxford University Press (UK).

Chang, Y., Kim, J. and Joo, J., 2013. An exploratory study on the evolution of design thinking: Comparison of Apple and Samsung. Design Management Journal, 8(1), pp.22-34.

Chatterjee, S. and Hadi, A.S., 2006. Simple linear regression. Regression Analysis by Example, Fourth Edition, pp.21-51.

Koch, K.R., 2013. Parameter estimation and hypothesis testing in linear models. Springer Science & Business Media.

Miranda, M., Ferreira, R., de Souza, C.R., Figueira Filho, F. and Singer, L., 2014, June. An exploratory study of the adoption of mobile development platforms by software engineers. In Proceedings of the 1st International Conference on Mobile Software Engineering and Systems (pp. 50-53). ACM.

Newcombe, R.G., 1998. Two?sided confidence intervals for the single proportion: comparison of seven methods. Statistics in medicine, 17(8), pp.857-872.

Peters, J.C., SAP SE, 2012. System and method for generating a pivot table. U.S. Patent Application 12/975,103.

Robbins, N.B., 2012. Creating more effective graphs. Wiley.

Samuels, M.L., Witmer, J.A. and Schaffner, A.A., 2012. Statistics for the life sciences. London: Pearson education. 

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