Analysis Of Smartphone Usage Amongst La Trobe University Students

Male and female proportion in sample

In this assignment we have analysed the usage of smartphone by the class of BUS1BAN of La Trobe University. For most of the analysis in this assignment a random data of the students was collected. For the selection of random data, a new variable “random number” was created. Randomly generated numbers were filled in the column. The first 100 random number from the lowest to the highest were selected for carrying out the analysis. The data involves the gender, phone usage and earnings of the students. The data also contains information on the smartphone the student possess. In addition, there is also information about the change in preferred brand of smartphone with increase in discount of Samsung Galaxy phone.

Part A

Gender	Proportion
Male Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	0.59
Female	0.41

Part B

Part C

From the selected sample we find that 59% of the students are males while 41% are females.

Part A

	Female	Male
Average Monthly Bill $	$79.15	$60.42

Part B

Part C

The average monthly bill of female students is $79.15, while the average monthly bill of male students is $60.42. Hence, we find that the average monthly bill of female students is higher as compared to male students.

Part A

	Female	Male
Average Monthly earnings	$1,108.87	$1,256.98

Part B

The above chart shows the relation between earnings and spending (on smartphone usage) of the students. From the chart it can be visualised that the higher the earning for male students the higher is the spending on smart phones.  

Part C

	Female	Male
Covariance	657.785	8434.711
Coefficient of Correlation	0.018	0.301
Coefficient of Determination	0.000	0.091
Y-Intercept	77.651	699.612
Slope	0.001	9.224
Least Square Line	Usage = 77.65+0.001*Earnings	Usage = 699.61+9.22*Earnings

Part D

The correlation between earnings and usage for female students is 0.018 while the for male students is 0.301. Hence, it is seen that the correlation between earnings and usage for male students is higher than female students. In addition, 9.1% of the usage on phones by males can be predicted from their earnings. However, the prediction level of usage from earnings for female students is very poor.

For each dollar increase in earnings of female students the usage on mobile phones increases by $0.001. For each dollar increase in earnings of male students the usage on mobile phones increases by $9.224. In the absence of any earnings female students spend $77.61 on phone usage. Similarly, in the absence of earnings male students spend $699.612 on phone usage.

Part A

Cross classification table by frequency

		Apple	Samsung	LG	Do not use mobile phone	Other Smart Phone	Basic Mobile Phone	Total
Gender	Male	37	13	1	0	8	0	59
Female	35	6	0	0	0	0	41
	Total	72	19	1	0	8	0	100

		Apple	Samsung	LG	Do not use mobile phone	Other Smart Phone	Basic Mobile Phone	Total
Gender	Male	0.37	0.13	0.01	0	0.08	0	0.59
Female	0.35	0.06	0	0	0	0	0.41
	Total	0.72	0.19	0.01	0	0.08	0	1

Part B

Part C

From the cross classification table, we find that the market shares for Apple phones is72%, while for Samsung it is 19%. The share of other smart phones is 8%. Thus, there is a huge difference in the market share of different smart phones.

Average monthly bill by gender

Moreover 37% of males use Apple iPhone while 13% use Samsung Galaxy. Further, 1% of the students use LG and another 8% use other smart phones.

35% of female students use Apple iPhone compared to 6% using Samsung Galaxy. Female students use either Apple iPhone or Samsung Galaxy.

Part A

	Apple	Samsung	LG	Do not use mobile phone	Other Smart Phone	Basic Mobile Phone	Total
Average Income	$1,144.91	$1,596.95	$150.00		$837.50		$1,196.25

Part B

From the chart it is seen that the average income of students possessing Samsung Galaxy is the highest. Students having Apple iPhone have a second-high income. Students having LG smartphone have the least average income. 

Part C

The students have been divided into three groups. Students in the low income group have an income below the 1^st quartile (Income). Students in the high income have an income above the 3^rd quartile.  

Income Level	Apple	Samsung	LG	Do not use mobile phone	Other Smart Phone	Basic Mobile Phone	Total
High	15	10	0	0	0	0	25
Medium	42	1	0	0	5	0	48
Low	15	8	1	0	3	0	27
Total	72	19	1	0	8	0	100

Income Level	Apple	Samsung	LG	Do not use mobile phone	Other Smart Phone	Basic Mobile Phone	Total
High	0.15	0.1	0	0	0	0	0.25
Medium	0.42	0.01	0	0	0.05	0	0.48
Low	0.15	0.08	0.01	0	0.03	0	0.27
Total	0.72	0.19	0.01	0	0.08	0	1

Part D

Part E

Most of the students possessing Apple iPhone are in the middle income group. There are equal number of students possessing Apple iPhone in both high and low income group.

Similarly, approximately equal number of students in the high and low income group possess Samsung Galaxy.  

Part A

Discount Offered on Samsung Galaxy	Proportion of Customers who said they will buy latest Samsung Galaxy
x	y
0%	0.24
5%	0.25
10%	0.25
15%	0.27
20%	0.31
25%	0.39
30%	0.46
35%	0.48
40%	0.61
45%	0.68
50%	0.72

Part B

From the above chart it is seen that with increase in discount for Samsung galaxy phones there is an increase in the proportion of students who would like to possess the phone.  

Part C

	Statistics
Covariance	0.026
Coefficient of Correlation	0.9658
Coefficient of Determination	0.9328
Y-Intercept	0.16
Slope	1.05
Least Square Line	y = 0.16+1.05*x

Part D

There is a strong correlation between discount and the proportion of students who say that they would like to have Samsung Galaxy phone, r = 0.9658. Moreover, 93.28% of the prediction of the change in usage can be predicted from the discount percentage.

Further, for 1% increase in Samsung Galaxy phone 1.05 students would change their use from Apple iPhone to Samsung Galaxy.

 The change is usage can be predicted from the equation

• Change = 0.16 + 1.05*Discount

Part A

Discount Offered on Samsung Galaxy	Proportion of Customers who said they will buy latest Samsung Galaxy
	Females	Males
x	yF	yM
0%	0.05	0.19
5%	0.05	0.2
10%	0.05	0.2
15%	0.07	0.2
20%	0.08	0.23
25%	0.1	0.29
30%	0.12	0.34
35%	0.13	0.35
40%	0.2	0.41
45%	0.23	0.45
50%	0.23	0.49

Part B

Part C

	Females	Males
Covariance	0.01	0.02
Coefficient of Correlation	0.9519	0.9676
Coefficient of Determination	0.9061	0.9363
Y-Intercept	0.018	0.144
Slope	0.405	0.644
Least Square Line	y = 0.018+0.405*x	y = 0.144+0.644*x

Part D

The correlation between discount and change with discount for females is 0.9519 while for males is 0.9676. Hence, it can be said that females are more loyal towards Apple Phone as compared to males.

For 1% increase in discount 0.405 females would change their loyalty. For 1% increase in discount 0.644 males would change their loyalty.

The change in loyalty for females can be given by the equation

• Change = 0.018+0.405*Discount

The change in loyalty for males can be given by the equation

• Change = 0.144+0.644*Discount

The change in loyalty for females has a prediction level of 90.61%. The change in loyalty for males has a prediction level of 93.63%.

Average monthly earning by gender

Part A

	Female	Male
Sample Proportion	0.478	0.522

The 95% confidence interval is calculated as =

Thus the standard error for students =

At 95% confidence interval

Thus, margin of error = 1.96*0.031 = 0.061

The proportion of female students = 0.478

Thus the lower limit of the confidence interval = 0.478-0.061 = 0.417

Thus the upper limit of the confidence interval = 0.478+0.061 = 0.539

Hence it can be said with 95% confidence that the proportion of female students for 2017 BUS1BAN class is between 0.417 and 0.539.

The proportion of male students = 0.522

Thus the lower limit of the confidence interval = 0.522-0.061 = 0.461

Thus the upper limit of the confidence interval = 0.522+0.061 = 0.583

Hence it can be said with 95% confidence that the proportion of male students for 2017 BUS1BAN class is between 0.461 and 0.583.

Part B

	Smart phone user
Sample Proportion	0.996

The 99% confidence interval is calculated as =

Thus the standard error for students =

At 99% confidence interval

Thus the margin of error = 0.01

Thus the lower limit of the confidence interval = 0.996 – 0.01 = 0.986

Thus the upper limit of the confidence interval = 0.996 + 0.01 ≈ 1

Hence, it can be said with 99% confidence that the proportion of students who use smart phones is between 0.986 and 1.

Part A

	Female	Male
Average Monthly Earnings	$1185.39	$1262.64

Part B

Females

The average monthly earnings of females = 1185.39

The standard deviation of the monthly earnings = 889.83

The number of female students in BUS1BAN Class = 121

The standard error of monthly earnings =

The margin of error = 1.96*80.89 = 158.55

Thus the lower limit of earning = 1185.39 – 158.55 = 1026.84

Thus the upper limit of earning = 1185.39 + 158.55 = 1343.94

Hence it can be said with 95% confidence that if another year of the BUS1BAN class is taken than the earnings of female students would lie between $1026.84 and $1343.94

Males

The average monthly earnings of males = 1262.64

The standard deviation of the monthly earnings = 918.60

The number of female students in BUS1BAN Class = 132

The standard error of monthly earnings =

The margin of error = 1.96*79.95 = 156.71

Thus the lower limit of earning = 1262.64 – 156.71 = 1105.93

Thus the upper limit of earning = 1262.64 +156.71 = 1419.35

Hence it can be said with 95% confidence that if another year of the BUS1BAN class is taken than the earnings of male students would lie between $1105.93 and $1419.35

Market share of smartphone brands by gender

According to the sample data 72% of the students of the class use Apple iPhone.

The US market survey claims the percentage of Apple iPhone users as 40%

Thus we have two proportions of Apple iPhone users. To test the claim we use the method for testing of proportions.

	BUS1BAN class	US market survey
Proportion of users	p1 = 0.72	p2 = 0.40
Sample size	n1 = 100	n2 = 100
Success rate	f1 = 72	f2 = 40

For testing the proportions

At 1% level of significance

Null Hypothesis: The share of Apple iPhone users at La Trobe is more than 40%

Alternate Hypothesis: The share of Apple iPhone users at La Trobe is not more than 40%

Significance Level: The significance level is 0.01. Hence if p-value for the test is less than 0.01 we reject Null hypothesis else we accept it.

Test Statistics: The test statistics = 4.5

Hence, p-value = 0.999

Conclusion: since p-value (0.999) is more than the significance level (a = 0.01) hence we fail to reject Null Hypothesis. Thus the share of Apple iPhone users at La Trobe University is more than 40% at 1% level of significance.

At 5% level of significance

Null Hypothesis: The share of Apple iPhone users at La Trobe is more than 40%

Alternate Hypothesis: The share of Apple iPhone users at La Trobe is not more than 40%

Significance Level: The significance level is 0.05. Hence if p-value for the test is less than 0.05 we reject Null hypothesis else we accept it.

Test Statistics: The test statistics = 4.5

Hence, p-value = 0.999

Conclusion: since p-value (0.999) is more than the significance level (a = 0.05) hence we fail to reject Null Hypothesis. Thus the share of Apple iPhone users at La Trobe University is more than 40% at 5% level of significance.

At 10% level of significance

Null Hypothesis: The share of Apple iPhone users at La Trobe is more than 40%

Alternate Hypothesis: The share of Apple iPhone users at La Trobe is not more than 40%

Significance Level: The significance level is 0.10. Hence if p-value for the test is less than 0.10 we reject Null hypothesis else we accept it.

Test Statistics: The test statistics = 4.5

Hence, p-value = 0.999

Conclusion: since p-value (0.999) is more than the significance level (a = 0.10) hence we fail to reject Null Hypothesis. Thus the share of Apple iPhone users at La Trobe University is more than 40% at 10% level of significance.

Here we present an analysis into the smartphone usage by the students of BUS1BAN class at La Trobe University.  

From the sample data it can be said that the proportion of males in the class is higher than the proportion of females. The average monthly bill of female students is higher than male students. The average monthly earnings of male students is higher than female students. In addition, the prediction rate of smartphone usage from monthly earnings is higher for males as compared to females. Moreover, for each dollar increase in earning the increase in usage of smartphone for male students of the class is higher than female students.

The investigation into the use of smartphone shows that most of the students (both males and females) use Apple iPhone. The analysis of the sample data shows that students with higher average earnings use Samsung Galaxy. We also find that equal number of students from high and low earnings use Apple iPhone.

With increase in discount for Samsung Galaxy the proportion of students (both females and males) who would like to use Samsung Galaxy gradually increases. The prediction rate for change in loyalty towards Samsung Galaxy with increase in discount is higher for male students than female students. Moreover, for 1% increase in discount the change in loyalty is higher for males than females.

We also find that the result of the US market survey to be true for the selected sample of students.

For the present assignment random sampling has been used to sample the students. The process of sampling is the most preferred sampling procedure since the method reduces any bias in the selection process. In addition, the sampling procedure is also the easiest. The analysis was done by taking sample data from BUS1AN class. To generalise it for La Trobe University, sample data for the university needs to be collected and analysed.

Reference

Anderson, D., Sweeney, D., Williams, T., Camm, J. and Cochran, J. (2017). Essentials of Statistics for Business and Economics. 8th ed. Cengage Learning.

Babin, B., Carr, J., Griffin, M. and Zikmund, W. (2012). Business research methods. 9th ed. Cengage Learning.

Black, K. (2016). Business Statistics: For Contemporary Decision Making, 9th Edition: For Contemporary Decision Making. 9th ed. Wiley.

Sharpe, N.R., DeVeaux, R.D. and Velleman P.F., 2012, Business Statistics, 2^nd Ed, Pearson Education