BUS105 Assignment: Statistical Analysis of Unisex Gym Preferences

This report analyzes customer preferences for a unisex gym based on a survey of 100 customers. It includes data summaries, calculations of confidence intervals and test statistics, and hypothesis tests to determine if a separate women-only gym should be established. The analysis covers variables such as gender, preference for unisex gyms, and time spent on cardio and weight machines. Key findings include the proportion of females preferring a unisex gym, the relationship between time spent on cardio and weight machines, and the statistical significance of gender-based preferences. The report also discusses the structure of a good statistical report and explains the hypothesis tests used, concluding with recommendations based on the statistical evidence. The report uses statistical tests to determine the significance of the data and supports the Gym Business XYZ to start a separate women-only gym.

Running head: BUS105 ASSIGNEMNT
BUS105 Assignment
Name of the Student:
Name of the University:
Author’s Note:

BUS105 ASSIGNEMNT
Table of Contents
“Section 1..............................................................................................................................................3
“Section 2..............................................................................................................................................5
“Section 3..............................................................................................................................................7
“Section 4..............................................................................................................................................9
“Section 5............................................................................................................................................11
“Section 6............................................................................................................................................11
“Section 7............................................................................................................................................11
References...........................................................................................................................................12
Appendix.............................................................................................................................................12

BUS105 ASSIGNEMNT
“Section 1
Reproduction of the data summaries including details of simple calculations
1a) Summary of the variable ‘do the customers want a unisex gym’ just considering the females”
Count of
gender Column Labels
Row Labels Female Grand Total
no 20 20
yes 33 33
Grand Total 53 53
As per the table, there are 53 females and 47 males from which 33 females want a unisex gym which
is more than 50% of the females. Hence, the unisex gym has more population of females than males.
“ 1b) Summary of the relationship between the variables ‘time on cardio machine’ and ‘time on
weight machine’”
0 10 20 30 40 50 60 70
0
10
20
30
40
50
f(x) = − 0.700584785647525 x + 34.3011108445893
R² = 0.772650147712829
Minutes spent on cardio and weight machine
Time spent on cardio
Time spent on weight
machine
The relationship between the time on cardio machine and time on weight machine can be drawn
using the scatter plot and depicting using a trendline. Both the variables have a negative correlation
depicting that as one spends more minutes on cardio would instil confidence the person; as a result,
the minutes of spending time on weight machine would be lesser. Hence, there is an inverse
proportion between the two; if minute spent on cardio increases then the minutes spent on weight
machine will decrease and vice versa.
“1c) Summary that lets you investigate the relationship between the variable ‘does the customer
want a unisex gym’ and ‘gender’”
Count of
gender Column Labels
Row Labels no yes Grand Total
Female 20 33 53

BUS105 ASSIGNEMNT
Male 32 15 47
Grand Total 52 48 100
Count of
Should the
gym be
Unisex? Column Labels
Row Labels no yes Grand Total
Female 37.74% 62.26% 100.00%
Male 68.09% 31.91% 100.00%
Grand Total 52.00% 48.00% 100.00%
The sample size depicts that the number who does not wants the unisex gym is greater than the
ones who want. On the contrary, there is contrary data between the gender. 62.26% of the female
proportion wants the gym to be unisex but the 68.09% of the males do not want the gym to be
unisex. As a result, females prefer the gym to be unisex being more in number and also as per
likeliness amongst gender.
“1d)Summary that lets you investigate the relationship between the variable ‘time spent on the
cardio machine ’ and ‘gender’”
Row Labels
Count of
gender
Average of Minutes on
Cardio
StdDev of Minutes on
Cardio
Female 53 37.9245283 15.14144726
Male 47 15.85106383 11.57767477
Grand Total 100 27.55 17.47285051
The count of female in the sample is more than males and as per the average minutes spent on
cardio is more for females because they 38 minutes whereas males spent approximately 16 minutes.
Moreover, the standard deviation figure is more for females because the variability of time is from
the average time spent. However, females have a directional relationship whereas males have a
inverse relationship with the time spent on cardio machine.

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“Section 2
Calculation of confidence intervals and test statistics
2a) Calculation of confidence interval for the proportion of females that prefer a Unisex gym using
my allocated sample”
Sample proportion for females at 90% CI
Should the Gym be Unisex as per the sample?
Gender no yes Grand Total
Female 20 33 53
Male 32 15 47
Grand Total 52 48 100
Number of Females = 53
Proportion of sample ^p = 33/53 = 0.622
Std Error of ^p = √ 0.622( 1−0.6 22)
53 =¿ 0.06660
90% Confidence interval =(Lower Limit, Upper Limit) = {(0.622 – (1.645*0.06660)), (0.622 +
(1.645*0.06660))}
 90% Confidence interval =(Lower Limit, Upper Limit) = (0.5124, 0.7315)
“2b) Calculation of confidence interval for the proportion of males that prefer a Unisex gym using my
allocated sample”
Sample proportion for males at 90% CI
Should the Gym be Unisex as per the sample?
Gender no yes Grand Total
Female 20 33 53
Male 32 15 47
Grand Total 52 48 100
Number of Males = 47
Proportion of sample ^p = 15/47 = 0.319
Std Error of ^p = √ 0.319(1−0. 319)
47 =¿ 0.06798
90% Confidence interval =(Lower Limit, Upper Limit) = {(0.319 – (1.645*0.0679)), (0.319 +
(1.645*0.0679))}

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 90% Confidence interval =(Lower Limit, Upper Limit) = (0.20730, 0.43069)
“2c) Calculation of Test stat for checking if the females that want a unisex gym is above 50% (Find
the sample proportion’s z score assuming p=0.5) using my allocated sample”
Test Statistics for p = 0.5
𝑧= 𝑝ො−𝑝
ට
𝑝(1−𝑝)
𝑛
Should the Gym be Unisex as per the sample?
Gender no yes Grand Total
Female 20 33 53
Male 32 15 47
Grand Total 52 48 100
Number of Females = 53
Proportion of sample ^p = 33/53 = 0.622
z= 0.6 22−0.5
√ 0.5 (1−0.5)
53
= 0.1 22
0.06 868 =1.7763
“2d) Calculation of Test stat for checking if the males that want a unisex gym is
above 50% (find the z score of proportion assuming p=0.5) using my allocated
sample”
Test Statistics for p = 0.5
𝑧= 𝑝ො−𝑝
ට
𝑝(1−𝑝)
𝑛
Should the Gym be Unisex as per the sample?
Gender no yes Grand Total
Female 20 33 53
Male 32 15 47
Grand Total 52 48 100
Number of Females = 53
Proportion of sample ^p = 33/53 = 0.622

BUS105 ASSIGNEMNT
z= 0.6 22−0.5
√ 0.5 (1−0.5)
53
= 0.1 22
0.06 868 =1.7763

BUS105 ASSIGNEMNT
“Section 3
Evidence I can decide the appropriate method to summarize data based on the nature of data (the
variable types)
a) My explanation why the different main findings in the sample report use different methods to
summarize data.”
The sample report uses variables as the nature and description of the data. The study in sample
report is to analyse “Whether there should be a unisex gym or not?”
Firstly, the survey questions were made pertaining to gender, likeliness/ preference for the unisex
gym and time spent on cardio and weight machines. Four variables are defined.
Variable Type of Data
Gender Categorical
Preference for unisex gym Categorical
Time spent on cardio machine Nominal (Quantitative)
Time spent on weight machine Nominal (Quantitative)
The summary of datasets is taken using pivot charts/ tables as the data can be summarized for
categorical variable and further percentage of the total to check for likeliness. For example if the
data set has two variable as “product version (Version A or Version B)” and “would the person buy it
(Yes or No)”. To consider the sample, pivot table is used and based on which a stacked bar graph is
made. The below table is added for understanding.
This helps in analysing the response in categorical variable with further proportion hypothesis
testing. Secondly, for two quantitative variable can be drawn using a scatter plot for two variables
like “distance travelled by the car” and its “selling price” which can enable to outline the trend
analysis using the equation.
The sample report produced the data in summarised and enable to understand so that neither
makes it difficult nor haphazard to examine the data set even if the sample size is big.
b) “My summary of an article that discusses gyms and an appropriate numerical summary using
my allocated sample from the section 3 dataset”

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Body shaming and gender differences are a common phenomenon where gender look decides the
body image such that a negative body image is given an ideal male/ female body image. Elíasdóttir
(2016), a graduate in psychology further ascertains that body image, body surveillance and esteem
is more highlighted in females than in males because that is socialization and further inspections
leading sexual objectifications. However, it is important to build a proper body image and improve
the wellbeing.
The same can be depicted by the sample taken for analysis where “variable 1 - gender” and
“variable 17 - are you ashamed of your body”, the two categorical data sets that are considered. The
results of the allocated sample are given as:
Count of
Gender Column Labels
Row Labels no yes
Grand
Total
female 11 35 46
male 41 13 54
Grand Total 52 48 100
Count of
Gender Column Labels
Row Labels no yes
Grand
Total
female 23.91%
76.09
% 100.00%
male 75.93%
24.07
% 100.00%
Grand Total 52.00%
48.00
% 100.00%
female male
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Gender and Body Shame
yes
no
The results depict that the females are more body shamed by the males. From 46 females, 35
females are ashamed of the body because of the socialization pressure and the comparison with the

BUS105 ASSIGNEMNT
ideal image body look. This constitutes to 76.09% whereas males 75.93% males are not ashamed of
their body and continue to have the body esteem as one has to.
“Section 4
Discussion of the webpages used to do all the calculation of a hypothesis tests
4a use a webpage to do a hypothesis test of the difference between two proportions using my
allocated sample
Using
http://www.socscistatistics.com/tests/ztest/Default2.aspx”
“4b) a use a webpage to do a hypothesis test of the difference between two means using my
allocated sample
Using
https://www.graphpad.com/quickcalcs/ttest1/?Format=SD”

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The results are:

BUS105 ASSIGNEMNT
“Section 5
Appropriate simple conclusions based on the computer output of hypothesis tests in section 4”
The results from the preference of unisex gym based on gender gives significant results depicting
that p is less than 0.05 level so making it a strong evidence (rejecting null hypothesis) that the
proportion is above 50% who would prefer unisex gym , such that most of females approve of the
same.
Secondly from the results of minutes on cardio machines in case of gender shows that the results is
less than 0.001 level, making it statistically significant with strong evidence (rejecting null
hypothesis) that the females spent more minutes on cardio machines such that the difference
between male and female is -22.073500 which is noteworthy for the results.
“Section 6
Demonstrates I can explain the structure of a good report that uses statistics”
The structure of the report needs to followed with basic criteria of introduction, background of the
study, data description, analysis and results with tables and charts, followed by recommendations
and conclusion. The references and appendix can make it complete. The overview of the report can
be given in an executive summary/ abstract. Also, the report needs to be presentable and organized
for best results.
The sample report is structured while adding executive summary even. However, there is one flaw in
the sample report such as headings like “recommendations and limitations” have not been
discussed. This can be further elaborated on ideas like “what other variables can be analysed” for
the study to be more put into practical use, followed by limitations like a set pattern is followed and
there is no scope of making it broad for a general public overview.
“Section 7
Demonstrates I can explain the hypothesis tests used in report and hypothesis testing in general”
The sample report discusses the hypothesis tests using preference to unisex gym with two different
tests, one with females and the other one with males defining the 50% proportion to be statistically
significant response.
For the hypothesis, Z score and p value is calculated, in this case p value is important to examine on
the study being valid. Here, p = 0.05 is taken stating that if the study is repeated for 100 times, then
95 times. The response on results would be the same. If the p value results in less than 0.05 then the
study is statistically significant.
The first hypothesis test on females was easy to understand as only one category of gender is taken
on preferability of unisex gym. The tests seem to have significant results on females wanting a unisex
gym with more than 50% of proportion. The computer results can be ascertain the manual
calculations done. The same can be done for the second hypothesis where other category of gender
that is males is taken. The results, in this case, have not come out to be significant because the
results are not valid at 0.05 level. The results not being significant on males wanting to have gym
does not support 50% of the proportion.