Descriptive Statistics of Quantitative Data - PDF

MODULE 7 UNIT 2
Activity
submission
© 2017 UCT / GetSmarter All Rights Reserved (not authorised for commercial use).

Learning outcomes:
LO2: Use descriptive statistics to analyse quantitative data.
LO3: Use inferential statistics to analyse quantitative data
Name:
1. Instructions and guidelines (Read carefully)
Instructions
1. Insert your name and surname in the space provided above, as well as in the file name.
Save the file as: First name Surname UCT BRA M7 U2 Activity Submission – e.g. Lilly
Smith UCT BRA M7 U2 Activity Submission. NB! Please ensure that you use the name
that appears in your student profile on the Online Campus.
2. Write all your answers in this document. There is an instruction that says, “Start writing
here” under each question. Please type your answer there.
3. Submit your assignment in Microsoft Word only. No other file types will be accepted.
4. Do not delete the plagiarism declaration or the assignment instructions and
guidelines. They must remain on your assignment when you submit.
PLEASE NOTE: Plagiarism cases will be penalised according to the Head Tutor and
GetSmarter's discretion.
IMPORTANT NOTICE: Please ensure that you have checked your course calendar for the due
date for this assignment. This calendar is available on the Online Campus and has also been
sent to you by your Course Coach.
Guidelines
1. There are six pages and five questions in this assignment.
2. Make sure that you have carefully read and fully understood the questions before
answering them. Answer the questions fully but concisely, and as directly as possible.
Follow all specific instructions for individual questions (e. g. “list”, “in point form”).
3. Answer all questions in your own words. Do not copy any text from the notes, readings
or other sources. The assignment must be your own work only.
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Plagiarism declaration:
1. I know that plagiarism is wrong. Plagiarism is to use another’s work and pretend that
it is one’s own.
2. This assignment is my own work.
3. I have not allowed, and will not allow, anyone to copy my work with the intention of
passing it off as his or her own work.
4. I acknowledge that copying someone else’s assignment (or part of it) is wrong, and
declare that my assignments are my own work.
2. Mark allocation
Each question receives a mark allocation. However, you will only receive a final percentage
mark and will not be given individual marks for each question. The mark allocation is there
to show you the weighting and length of each question.
Question 1 4
Question 2 8
Question 3 8
Question 4 4
Question 5 6
TOTAL 30
3. Assignment questions
Note:
Ensure that you have downloaded the Microsoft Excel data set (available in the Module
Downloads folder) and have it available before you attempt this assignment. In addition,
you can use Excel to complete your calculations and then transfer your answers in the
spaces provided in this document.
Note for Macintosh users: If you are using Microsoft Excel 2011, the data analysis toolkit is
unavailable to you. You need to update your version of Excel or use another spreadsheet
application.
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The questions in this activity submission are based on the following case study.
The Walk-in Closet (continued from Module 6):
Samantha Jones, the CEO and founder of Walk-in Closet (a boutique women’s fashion
retailer based in Johannesburg), is looking to expand her retail business to an online
environment. The business has three stores in Gauteng, and Sam is in the process of
opening up a new store in Cape Town’s trendy Cape Quarter. The stores are doing well, but
the recently-launched online website is not doing as well as hoped. The website was
developed in record time and, in theory, the online presence is the right move for the
business, as it allows for expansion into both the national and international market, while
also keeping overheads low. She is able to fulfil each order from stock available at her
existing stores, and as the demand increases in a particular region, she considers opening a
new physical store.
There is some new growth in the customer base during the first few months. However,
Sam’s greatest fear is that she will lose loyal customers from her physical stores, and that
although profit is increasing due to the lower cost of online sales, she finds her turnover
remaining relatively constant. As it turns out, she is able to attract a number of new
customers, especially in Cape Town, where Walk-in Closet doesn’t yet have a physical store.
Sam needs to gain a greater understanding of her customers’ experiences with the website.
In order to do this, she commissions a focus group to be run in Cape Town by one of her
trusted suppliers and partners. This partner gathers four local customers to chat about their
experiences with the website to hopefully provide some insights into the online experience,
which can then be used to improve the website. Due to the limited available funds for
research, Sam asks a local university professor if his research students might be interested
in doing an analysis of the data as a class project. Sam agrees to provide a video and written
transcript of the focus group in which the students can conduct a thematic analysis of the
data and provide some insights, which Sam could then use to make further decisions.
Based on the success of the focus group project and the work that is done by the university
students, Sam decides to conduct another research project. She doesn’t want to take her
focus off of the retail stores, so she asks each of her store managers to conduct customer
satisfaction surveys at their outlets. All surveys are collected on the same day during the
same one-hour period to ensure consistency. Thirty-five surveys are completed and these
are captured into a Microsoft Excel spreadsheet. Sam once again asks the university
professor if his students can assist with the analysis. She wants to gain a better
understanding of whether her customer service levels are up to standard.
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Question 1
Conduct a percentage and frequency distribution based on:
1.1 Suburb (Round off your answers to two decimal places.)
Start writing here:
Suburb
Frequency
distribution
% frequency
distribution
East 12 33.33%
North 9 25.00%
South 4 11.11%
South 3 8.33%
West 8 22.22%
Grand
Total 36 100.00%
Table 1
1.2 Gender (Round off your answers to two decimal places.)
Start writing here:
GENDER Frequency Percentage frequency
Female 17 47.22%
Male 19 52.77%
Grand Total 36 100.00%
Table 2
Question 2
Calculate the mean, median, and mode for:
2.1 All customers by age (Round off your answers to two decimal places.)
Start writing here:
Age summary statistics
Age
Mean 44.47
Median 44.00
Mode 52.00
Table 3
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2.2 All customers by average spend (Round off your answers to two decimal places.)
Start writing here:
Ave Spend (PA)
Mean 4386.28
Median 3594.5
Mode 6106
Table 4
Question 3
Calculate the range, standard deviation, and variance for:
3.1 Age (Round off your answers to two decimal places.)
Start writing here:
Age descriptive statistics
Standard Deviation 10.83
Sample Variance 117.23
Range 40.00
Table 5
3.2 Average spending (Round off your answers to two decimal places.)
Start writing here:
Ave Spend (PA) Summary
statistics
Standard Deviation 2340.13
Sample Variance
5476197.1
8
Range 7423.00
Table 6
Question 4
The survey questions represented in the dataset were as follows. The scale used was 1 (least
agree) to 5 (most agree):
 Question 1: This is my clothing store of preference.
 Question 2: This store always has something for me to purchase.
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 Question 3: My size is always available in each style.
 Question 4: I always get attentive service at this store.
 Question 5: I’ll recommend this store to my friends.
The survey is intended to measure overall attitude towards the store.
Using an independent samples t-test, test the following hypothesis: There is a higher
preference amongst females than males. (Remember to calculate your average survey
variable.) (Include the Excel output that you have calculated, and highlight the p-value and
all other relevant output.)
Start writing here:
Hypothesis
H0: There is no difference in preference among males and females
Versus
H1: There is a higher preference amongst females than males.
T-test result table
t-Test: Two-Sample Assuming Unequal Variances
FEMALE MALE
Mean 2.929411765 3.031578947
Variance 0.529705882 0.352280702
Observations 17 19
Hypothesized Mean Difference 0
df 31
t Stat -0.458281252
P(T<=t) one-tail 0.324973482
t Critical one-tail 1.695518783
P(T<=t) two-tail 0.649946964
t Critical two-tail 2.039513446
Table 7
Since the p-value (0.32) is greater than the level of significance (0.05), the decision
rule is to not to reject the null hypothesis. It is therefore concluded that there is no
difference in preference among males and females.
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Question 5
5.1 Use correlation to test the following hypothesis: Average spend is positively correlated
to the mean survey score. (Include the Excel output that you have calculated, and highlight
the p-value and all other relevant output.)
Start writing here:
Regression Statistics
Multiple R 0.009623138
R Square 9.26048E-05
Adjusted R Square -0.02931644
Standard Error 2374.181915
Observations 36
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%
Intercept 4489.210448 1876.522 2.392304 0.022415 675.659 8302.762
Mean survey score -34.502571 614.8585 -0.05611 0.955579 -1284.05 1215.04
Table 8
There is a very weak negative correlation between average amount spent and mean survey
score.
5.2 What is the relationship (correlation) between average spend and question four: I
always get attentive service at this store. (Include the Excel output that you have
calculated, and highlight the p-value and all other relevant output.)
Start writing here:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.099486
R Square 0.009897
Adjusted R Square -0.01922
Standard Error 2362.513
Observations 36
CoefficientsStandard Error t Stat P-value Lower 95% Upper 95%
Intercept 4826.018 850.8751 5.671829 2.3E-06 3096.832 6555.204
-153.696 263.634 -0.58299 0.563748 -689.464 382.0731
Table 9
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