Research Project 2 BUS1BAN 2019 2019 1007 PDF

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LA TROBE UNIVERSITY
BUS1BAN ANALYSING BUSINESS DATA LA TROBE UNIVERSITY
BUS1BAN ANALYSING BUSINESS DATA...

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1902 BUS1BAN BU/BE/MI/SH/C3

LA TROBE UNIVERSITY BUS1BAN ANALYSING BUSINESS DATA Semester 2, 2019 Research Project Two Due Date: 5pm 27th October

Instructions 1. Fill in your name, student ID, contribution (100% should be specified for each group member in most cases) in the table above on the cover page. 2. Each group member must sign on the cover page to show your agreement on the version of your group work to be submitted. 3. Record your subject tutor’s name and workshop details under your group member information. 4.

Research Project 2 carries 26 marks and will represent 13% of your final grade.

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An insight into market share and usage of mobile phones by students studying BUS1BAN at La Trobe University Use the random sample of 100 observations and answer Questions 1-10 in Part A to Part C. Note: Students who completed Research Project 1 as a group should remain in the same group for Research Project 2 using the same random sample, unless otherwise approved by the subject coordinator in writing. Part A: Point Estimate and Confidence Interval Q1. Suppose you randomly select a student from BUS1BAN class, how likely is it that the student selected will be a female student? How likely is it that the student selected will be an iPhone user? [1 mark]

Female students iPhone users

Proportion in percentage form ( ^p ) 54/100=0.54, 0.54*100=54%, 54% or 0.54 70/100=0.70, 0.70*100=70%, 70% or 0.70

Q2. Estimate the 99% confidence interval for the proportion of iPhone users. Show the confidence intervals graphically and interpret your results. You should show the formula and calculation by putting values in the formula. [2 marks] Sample size: 100 Sample proportion: p = 70/100 = 0.07 Required condition: 100 x 0.07 = 7 Required condition: 100 x 7 Sample standard deviation: 20.35 t-value: 0.386 Lower confidence limit: 6.21 Upper confidence limit: 7.79

According to the graph above, our estimate shows that the 99% confidence level of students selected being an iPhone user is estimated to be between 6.21 and 7.79

Q3. What are the average monthly earnings of male and female students in your sample? [1 mark] Average monthly earnings in dollars ($) Female students Male students

$1,234.48 $1,417.32

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Q4. Provide 95% confidence interval of the average monthly earnings for each gender. Show the confidence intervals graphically and interpret your answer. You should show the formula and calculation by putting values in the formula. [2 marks] Females:

s

Sample Standard Deviation Sample size "Tail" probability Sample mean (point estimate) t-value

n α

857.97 54 5%

tα/2,n-1

1234.48 2.006

LCL UCL

857.97 = 1000.30 √ 54 857.97  1234.48+2.006 = 1468.66 √ 54

 1234.48−2.006

THE 95% Interval estimate is between 1000.30 and 1468.66. THE 95% interval suggests that the average earnings are above 1000.30.

Males:

s

Sample Standard Deviation Sample size "Tail" probability Sample mean (point estimate) t-value

LCL UCL

n α

995.46 46 5%

tα/2,n-1

1417.32 2.014

1712.94 =1121.70 √ 46 857.97 =1712.94  1234.48+2.006 √ 54

 1121.70−2.014

THE 95% Interval estimate is between 1121.70 and 1712.94. THE 95% interval suggests that the average earnings are above 1121.70.

Part B: Hypothesis Testing Q5. A US market survey shows that the market share of iPhone is more than 50% of the US market. Is it true for BUS1BAN students at La Trobe as well? Use your sample data to test this claim at the 5% level of significance and interpret your answer. [5 marks] Note: You should label and follow the five steps of hypothesis testing procedure. Page 3 of 6

1. Hypotheses: Null hypothesis (H0) μ=¿ 0.50 Alternative hypothesis (HA) μ>¿ 0.50 2. Identify/calculate the test statistic • Use z-statistics if � is known (Normal population, or n >=30) • Use t-statistics if � is unknown (Normal population) 3. Specify the significance level (α) and identify the decision rule (rejection region) 4. Make decision (reject H 0 if the test statistic lie in the rejection region, otherwise do not reject H 0 ) 5. Write conclusion

Part C: The Effect of Price on Preference Q6. 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 in your random sample. [4 marks] Discount offered on Samsung Galaxy (i.e. if the Galaxy is X cheaper than the iPhone) X 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Proportion (%) of male students who said they would buy the latest Samsung Galaxy instead of the latest iPhone if the price of Samsung Galaxy is discounted by X. Y 28 33 26 35 43 50 59 59 65 65 72

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Q7. Based on your Q6 results, perform a simple linear regression of variable Y on variable X using Excel. Report the Excel regression output below, and write down the linear regression equation under the Excel regression output. [3 marks]

y =

Y 80 70

f(x) = 96.18 x + 24.59

60 50 40 30 20 10 0 0%

10%

20%

30%

40%

50%

60%

96.182x + 24.591 Page 5 of 6

Q8. Interpret the intercept, slope coefficient, and coefficient of determination in Q7. Then compute the correlation coefficient between X and Y using the value of coefficient of determination. [4 marks] Intercept is 24.59, this shows that the amount of people wanting to buy a new Samsung when the phone has a 0% discount is 24.59. Slope coefficient 96.18 shows that as the discount increases there is a increase on the demand of the new Samsung. Coefficient of determination 0.942733459 shows us that 94% of the variation in the proportion of male students switching to the new Samsung can be explained. Correlation coefficient is the square root of 0.942733459 which equals to 0.97, meaning the correlation is close to a linear correlation. Q9. Based on the regression results in Q7, is there a significant relation between X and Y? Explain why. [2 marks] Ther el at i ons hi pbet weenXandYi sv er ysi gni ficantas ,es pec i al l yast hecor r el at i on coeffic i enti sabov e1.Thi smeanst hatt her el at i ons hi pi sl i nearposi t i v e.Basedont he r egr es si onr esul t s ,i ti sc l eart hatdi scountoffer edi nc r eases/ decr easesX,andt henumber ofmal eswant i ngt obuyaSams ungphonei nc r eas es/ dec r eases. Part D: Summary and Discussion Q10. What are your main findings/conclusions based on the analysis in Q5-Q9 of Parts B and C. [2 marks]

The main findings we have found that is there is a major positive linear relationship in males being willing to buy a Samsung on discount instead of an iPhone, in question 6. When there is a discount on the Samsung phones, there is a large demand on males wanting to purchase the Samsung phone.

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