Business Statistics Assignment Part B

Complete the Business Statistics Assignment Part B and submit it on time. The assignment includes hypothesis testing, regression analysis and index number calculation. The subject is Business Statistics and the course code is ACTY 5401 under Bachelor of Business. The assignment is to be submitted in Semester 2, 2018. Contact Student Learning and Achievement, Maia Maori Centre or Pacific Centre for academic support.

Business and Enterprise Network
Business Practice Pathway
Bachelor of Business
ACTY 5401 Business Statistics
Assignment Part B
Semester: Semester 2, 2018
Date issued: Thursday, 20 September 2018
Due date: Saturday, 3 November 2018; 11:55pm
Delivery: Submit your WORD file to Moodle by the due date and time.
Total marks: 40 marks
Weighting: 20% of course
Instructions:  Complete this template, including cover sheet.
 Insert ALL answers, including tables and charts from Excel into this
Word template. Text answers should be in the blue font provided.
 Do NOT remove the questions from this template.
 Where applicable, show details of your workings.
 This is an individual assignment and must be your own work.
Collusion, copying or plagiarism may result in disciplinary action.
Student Name: Jitesh Prasad
Student ID No: 1390182
Lecturer: Keith Rankin
Student declaration: I confirm that:
 This is an original assessment and is entirely my own work.
 Where I have used ideas, tables, diagrams etc. of other writers,
I have acknowledged the source in every case.
 This assignment has not previously been submitted as assessed
work for any academic course.
Signature: in font jiteshprasad
Date of signature: ...
Do you want to do the best that you can do on this assignment? You could contact:
Student Learning and Achievement
https://www.unitec.ac.nz/current-students/study-support/student-learning-and-achievement
Maia Maori Centre
https://www.unitec.ac.nz/maori/maia-centre-and-marae/maia-maori-centre
Pacific Centre
https://www.unitec.ac.nz/pacific/who-we-are/pacific-centre
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QUESTION 3: HYPOTHESIS TEST (PART B) 16 MARKS
A large sample from the 2011 New Zealand Income Survey is available from:
http://archive.stats.govt.nz/~/media/Statistics/services/microdata-access/nzis11-cart-surf/
nzis11-cart-surf.csv.
Save this as an Excel file. You will also need the Data Dictionary from:
http://archive.stats.govt.nz/~/media/Statistics/services/microdata-access/nzis11-cart-surf/
nzis11-cart-surf-data-dic.xls to decode category data such as region and gender.
The Department of Labour is interested in whether there is a difference between the mean
weekly income of workers by age and region. Using the sub-SURF Survey data, you should
conduct the appropriate test to establish whether, for your allocated region, the mean weekly
income of young female workers (aged 25-34) was different than for older female workers
(aged 55-64). Include only people working from 30 to 40 hours per week
To determine the region to use, calculate in Excel =MOD (student ID,11) + 1.
Your allocated educational category will be the one that corresponds to the calculation result.
1 Northland
2 Auckland
3 Waikato
4 Bay of Plenty
5 Hawkes Bay
6 Taranaki
7 Manawatu
8 Wellington
9 Nelson
10 Canterbury
11 Otago
For this task, you will filter your raw data by 'sex', ‘age’, ‘region [lgr]’, and 'hours worked'.
[Remember you need to copy filtered data to a new worksheet.]
You will then sort your data by age.
Any tables or charts should be produced in Excel, and then copied into this Word template.
a) State the hypotheses that you are testing. [3 marks]
Null hypothesis H0 : μYoung female workers =μOlder female workers
Alternative hypothesis H1 : μYoung female workers ≠ μOlder female workers
b) Suggest a reason why a researcher might think average incomes of young-adult female
workers might differ from older-aged female workers. [1 mark]
The income might differ owing to the difference in experience which tends to lead to higher income
for the older aged employees.
c) Produce an appropriately formatted 2 sample t-test equal variance output table.
Include, in your table, the level of significance for your test. [3 marks]
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Level of significance = 0.01 (as per the formula and STUDENT ID)
d) From your table, determine the significance of your test result, using both the critical value
method and the p-value method. [3 marks]
The t stat (-1.35) tends to lie between the two tail critical value interval (-2.62 to 2.62) and hence
the null hypothesis cannot be rejected which implies that the result is not significant.
The p value two tail is 0.18 which is higher than the 0.01 level of significance and hence the
available evidence is insufficient to reject the null hypothesis which implies non-significance of the
result
e) State your conclusion. [1 mark]
Based on the above hypothesis testing, it can be concluded that the average weekly wages of the
younger women (age group 25-34 years) does not differ from the corresponding weekly average
wages of the older women (age group 55-64 years).
f) Using data from your table in (c), calculate the confidence interval for the difference in
average weekly income, for your allocated region, between younger and older female
workers. [3 marks]
Difference of mean = 978.557 – 1078.76 = -100.208
Pooled standard deviation = sqrt(pooled variance) =414.411
N1 =61, N2 =64
The two tailed t value for 95% confidence interval = 1.9794
Upper limit = (-100.208) + (1.9794 * 414.411 * sqrt ((1/61) + (1/64))) = 46.57
Lower limit = (-100.208) - (1.9794 * 414.411 * sqrt ((1/61) + (1/64))) = -246.99
95% confidene interval = [-246.99 46.57]
g) Comment on whether an equal-variance test was the most appropriate test, given your data.
[1 mark]
Equal variance test is the appropriate test considering the fact that the number of observations for
both groups is quite similar and also the variance is very similar.,
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h) Suggest any other variable (ie not relating to gender or working hours) that might influence
mean weekly incomes for your selected region. [1 mark]
A crucial variable which could influence the mean weekly incomes could be the experience
indicated by the years of full time work.
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QUESTION 4: REGRESSION (PART B) 18 MARKS
The Department of Labour is also interested in, for each region, the relationships between
incomes, gender, and hours worked per week for those people of specific ethnicities.
For this, using the same downloaded set of data as in Question 3, you will filter by 'ethnicity' and
‘region’, using the same region as in Q3. (Remove the 'sex', 'age' and 'hours' filters.)
To determine your assignment ethnicity calculate, in Excel, =MOD(student ID,4)+1.
Your allocated ethnicity will be the one that corresponds to the calculation result. Your
allocated category will be this ethnicity combined with your region from Q3.
Ethnicities
1 Pacific
2 Maori
3 European
4 Asian
Using the same downloaded set of data as in Question 3, you are required to:
a) Create a scatterplot with fitted linear trend-line, to see if there is a linear relationship between
hours-worked (x) and income (y) of the people with your allocated category.
Your Excel-created chart should include the Excel-calculated least-squares linear regression
equation ('trendline', appropriately edited), plus your name as a digital signature (in blue, in
English letters, and in a different font). [5 marks]
0 10 20 30 40 50 60
0
500
1000
1500
2000
2500
3000
f(x) = 15.5856676322751 x + 290.343706007873
R² = 0.327875389647962
Scatter Plot
Hours Worked (Hrs)
Income (NZD)
b) Comment on whether you see a linear association between hours-worked and income.
[1 mark]
It is apparent that there is significant deviation of the scatter plot points from the trend-line and
hence the association between the variables seems to be non-linear.
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You consider adding another variable, gender, to help explain variation in people's incomes.
Use the Data Analysis Toolpak in Excel to conduct a multiple regression to examine the effect of
'weekly hours worked' and 'sex' on the weekly incomes of the people in your allocated category.
You should present:
c) your edited regression results table [2½ marks]
d) the resulting regression equation [1½ marks]
Income = 93.17 + (15.80* Hours) + (134.28* Sex)
e) Interpret the meaning of each of the independent variable coefficients. [not the intercept]
[2 marks]
The hours slope coefficient is 15.80 which implies that as the hour worked increased by 1 hour, the
income would increase by $ 15.80 on an average.
The sex slope coefficient is 134.28 which implies that females on average are paid $ 134.28 more
than their male counterparts.
f) Comment on your regression results with respect to:
 the overall explanatory power of the multiple regression [1 mark]
 differences in the statistical significance of each of the two independent variables
[2 marks]
The R square value is 0.3447 which implies that the independent variables jointly can offer
explanation to 34.47% of the movements in the dependent variable (i.e. income).
The p value for hours slope coefficient is 0 where the corresponding value for sex slope coefficient
is 0.33. This implies that hours is a significant variable whose slope cannot be assumed bas zero
where the slope of sex variable can be taken as zero.
g) Use your regression to predict the income for a female in your allocated category, who
works zero hours.
You should include a comment about the reliability of your prediction. [2 marks]
Female (Sex) = 2
Hours worked = 0 hours
Income = ?
Income = 93.17 + (15.80* 0) + (134.28* 2)
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Income = 361.72 (NZD)
h) Comment on one of the assumptions you could examine to check on the overall validity of
your multiple linear regression model. [Do not produce a chart.] [1 mark]
…
The residual plot could be used to ascertain if the assumption about homoscedasticity is fulfilled or
not. It can also be used to determine if the distribution of the residuals is normal or not.
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QUESTION 5: INDEX NUMBERS (PART B) 6 MARKS
a) Create two Simple Relative Index Number Series – one for your industry, one for all
industries – from the hourly wage data you used in Question 2 (Part A). Use only your
quarterly data from 2007Q4 to 2017Q4, with 2007Q4 as your base period. [3 marks]
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b) Using only your two index numbers for 2017Q4, decide whether hourly wages in your
selected industry increased (or decreased) proportionally more than other industries in
the decade from the end of 2007 to the end of 2017. [1 mark]
The index number for my assigned industry (Education and Training) for 2017Q4 is 125.63 in
comparison to 131.37 for all the industries. Hence, it is apparent that hourly wages has decreased
proportionally to the increase in the other industries.
c) Using only your index numbers for 2012Q4 and 2017Q4, calculate annual average
increase of hourly wages in your industry, and in all industries, for your 5-years of data.
[2 marks]
Index number (Education & Training) 2012 Q4 = 113.52
Index number (Education & Training) 2017 Q4 = 125.63
Annual average increase in wages (Education & Training) = [(125.63-113.52)/113.52]*(100/5) =
2.13%
Index number (Total all Industries) 2012 Q4 =116.67
Index number (Total all Industries) 2017 Q4 = 131.37
Annual average increase in wages (Total all Industries) = [(131.37-116.67)/116.67]*(100/5) =
2.52%
Grading Note:
Half-marks will be deducted for mistakes and omissions.
Not all markers' comments will incur a loss of marks.
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