Why the Gym Business XYZ should start a separate women only gym after it had sufficient growth.
Executive summary
Gym Business XYZ is planning to expand by purchasing an extra smaller nea
y location, based on this report it should make the new small gym a Unisex Gym that will only serve females.
Contents
Background and data set 2
Methods used to analyse the survey data 3
Main findings 4
Confidence intervals 6
Hypothesis tests that support the main findings 7
Conclusion 16
Appendix part 1 data set 17
Appendix part 2 notes on hypothesis testing 20
Appendix 3 regression formula 24
Background and data set
In Australia there are many women only gyms and since Gym Business XYZ has been successful enough to expand into a small new premises customers were given a survey to determine if the new gym should be a unisex gym.
A sample of 100 customers were given the following survey
Survey question 1: Are you male or female?
This question should be thought of a is a categorical variable, because the answer is one of the categories “male” or “female”
Survey question 2: Would you prefer if the gym was unisex in other words
if you are man would you prefer a gym with only men, yes or no?
if you are woman would you prefer a gym with only women, yes or no?
This question should be thought of a is a categorical variable, because the answer is one of 2 categories
Survey question 3: How much time do you spend on the cardio machine (in minutes)?
This question should be thought of as a Quantitative variable because it records the quantity (amount) of time spent on the machine
Survey question 4: How much time do you spend on the weight machine (in minutes)?
This question should be thought of as a Quantitative variable because it records the quantity (amount) of time spent on the weight machine
The answers to the survey are available from appendix 1
Methods used to analyse the survey data
This report will use
*Simple descriptive statistics
*Confidence intervals
*Hypothesis tests
Going into more detail
Simple descriptive statistics : Descriptive statistics are numbers and graphs that summarize sample. In our case the descriptive statistics are the sample mean, proportion, slope and intercept. The graphs are bar charts to compare proportions and a scatterplot to show the relationship between two quantitative variables.
Confidence intervals:
Confidence intervals are found for the following parameters related to the report
*Just considering the females, what proportion of females want a unisex gym.
*Just considering the males, what proportion of males want a unisex gym.
Hypothesis tests :
The main findings of this report are related to the following Hypotheses
*Do most women want a Unisex gym?
*Do Most men want a Unisex gym?
*Is there a relationship between the variables “Gender” and “Reason for going to the gym”
*Is there a relationship between the variables “Time on weight machine” and “Time on cardio machine”
This report uses Hypothesis tests to check if there is strong evidence for a hypothesis test Refer to appendix 2 for notes on hypothesis testing
Main findings
Females are more likely to prefer a unisex gym
This is obvious if you look at summary of the answers to survey questions
Survey question 1: Are you male or female?
Survey question 2: Would you prefer if the gym was unisex
Should the gym by unisex
Row Labels
No
yes
Grand Total
Female
21
39
60
Male
32
8
40
Grand Total
53
47
100
Count of Should the gym be Unisex?
Column Labels
Row Labels
no
Yes
Grand Total
Female
35.00%
65.00%
100.00%
Male
80.00%
20.00%
100.00%
Grand Total
53.00%
47.00%
100.00%
65% of the females want the gym to be unisex, however only 20% of males want a unisex gym, So 65%-20%=45% more women want the gym to be Unisex
Females spend more time on the cardio machine
This is obvious if you look at summary of the answers to survey questions
Survey question 1: Are you male or female?
Survey question 3: How much time do you spend on the cardio machine?
Row Labels
Count of gende
Average of Minutes on Cardio
StdDev of Minutes on Cardio
Female
60
XXXXXXXXXX
XXXXXXXXXX
Male
40
13.625
XXXXXXXXXX
Grand Total
100
28
XXXXXXXXXX
Females spent an average of 38 minutes on the cardio machine and males only spent an average of 14 minutes. So females spend 38-14=24 minutes more on average
As time spent on cardio machine increases the time spend on the weight machine decreases
This is obvious if you look at scatterplot that shows answers to survey questions
Survey question 3: How much time do you spend on the cardio machine?
Survey question 4: How much time do you spend on the weight machine?
As the time spent on the cardio machine increases the time spent on the weight decreases
Confidence intervals
Confidence intervals fo
The proportion of females that want a unisex gym
The proportion of males that want a unisex gym.
90% confidence interval for sample proportion for females
Should the gym by unisex
Row Labels
No
yes
Grand Total
Female
21
39
60
Male
32
8
40
Grand Total
53
47
100
Just considering the females
n=60,
sample proportion = 39/60=0.65
standard e
or of sample proportion = XXXXXXXXXX
90% confident the true proportion is between
XXXXXXXXXX* XXXXXXXXXX=0.55 and XXXXXXXXXX* XXXXXXXXXX=0.75
90% confidence interval for sample proportion for males
Should the gym by unisex
Row Labels
No
yes
Grand Total
Female
21
39
60
Male
32
8
40
Grand Total
53
47
100
Just considering the males
n=60,
sample proportion = 8/40=0.2
standard e
or of sample proportion = XXXXXXXXXX
90% confident the true proportion is between
XXXXXXXXXX* XXXXXXXXXX =0.095 and XXXXXXXXXX* XXXXXXXXXX=0.305
Hypothesis tests that support the main findings
Before giving the survey to the gym customer we knew we wanted to answer the question
“Do most of the females want a unisex gym?”
Which gives us the null and alternative hypothesis
H0 :p≤0.5 (to find the test stat assume p=0.5) HA :p>0.5
So we use the test stat
Should the gym by unisex
Row Labels
No
yes
Grand Total
Female
21
39
60
Male
32
8
40
Grand Total
53
47
100
n=60,
sample proportion = 39/60=0.65
=
The p-value is P(Z>2.324) =0.01
Checking the entire process using a webpage we get the same result.
Since the p-value is less than 0.05 we reject H0 because there is strong evidence the proportion is above 50% , So most of the females want a unisex gym.
Test of the hypothesis “Do most of the males prefer a unisex gym”
Before giving the survey to the gym customers it was clear that summary of the dataset based on the survey can be used to answer the question “Do most of the males want a unisex gym?”
Which gives us the null and alternative hypothesis
H0 :p≤0.5 (assume p=0.5 to find the test stat) HA :p>0.5
So use the test stat
Should the gym by unisex
Row Labels
No
yes
Grand Total
Female
21
39
60
Male
32
8
40
Grand Total
53
47
100
just considering the males n=40,
sample proportion =8/40=0.2
=
The p-value is P(Z>-3.7947) = XXXXXXXXXX
Checking the entire process using a webpage we get the same result.
Since the p-value is less than 0.05 we do not reject H0 There is not strong evidence most of the males want a unisex gym.
Hypothesis test comparing proportions
Before giving the survey to the customers, it is was clear that the summary of the dataset can be used to answer to the question
“Is there a relationship between variables ‘gender’ and ‘should the gym be unisex’ “
So the appropriate null and alternative hypothesis is
H0 :p1= p2 HA :p1≠ p2
the appropriate test stat formula is
where
since you assume H0 is true this becomes
Using the information from the sample = 4.41
p-value is P(Z<-4.41)+P(Z>4.41)=0.000
Verfifying the results with an online webpage
http:
www.socscistatistics.com/tests/ztest/Default2.aspx
Hypothesis test comparing means
Before giving the survey to the customers, it is was clear that the summary of the dataset can be used to answer to the question
“Is there a relationship between variables ‘gender’ and ‘time on cardio machine’ “
So the appropriate null and alternative hypothesis is
H0 :µ1= µ2 HA :µ1≠ µ2
The appropriate test statistic is
which has a t distribution with df
Since you assume H0 is true to calculate the test stat, the test stat becomes
Using the results from the surveys
Row Labels
Count of gende
Average of Minutes on Cardio
StdDev of Minutes on Cardio
Female
60
XXXXXXXXXX
XXXXXXXXXX
Male
40
13.625
XXXXXXXXXX
Grand Total
100
28
XXXXXXXXXX
=94 test stat = 8.08
p-value is P(t< XXXXXXXXXXP(t>8.08)=0.000
P-value 0.000
Verifying the results with the webpage
https:
www.graphpad.com/quickcalcs/ttest1/?Format=SD
data entry
Computer output
Reject H0 there is strong evidence there is a difference between means
Before getting the survey you can ask the questions
Is there a relationship between variables.
Answer:
The test stat is
Since you assume the null hypothesis is true the test stat becomes
Test stat=
The formulas for and are very complicated. (refer to appendix 3)
Using computer output
Coefficients
Standard E
o
t Stat
P-value
Intercept
XXXXXXXXXX
Minutes on Cardio
XXXXXXXXXX
XXXXXXXXXX
-20.1
1.07E-36
Test stat=
p-value is P(t< XXXXXXXXXXP(t>20.1)=1.07E-36
Information about women only gyms taken from the competitions webpages
“Why Women-Only Gyms Are More Ideal For Women Who Want To Stay Fit
Hitting up the gym could be one of the best solutions for women who want to commit to a healthier lifestyle. Since home exercise videos can be easily replaced by regular morning talk shows, it’s sometimes easier to just resort to a gym to stay on track. However, not a lot of women like the idea of losing weight while being su
ounded by men. Many gyms cater to the needs of both men and women, but exclusive women’s gyms hold certain advantages, which could ultimately give women better results.
Comfortable and Appropriate
Women’s gym provide the ideal space for workouts, without the distu
ance of working out around men. The gym is used as a place for doing workouts, and not as a dating venue. So, if you want to concentrate on doing your workouts in peace, a gym with female-only members is a much better option. Secondly, when you are not in shape, it is much more emba
assing to do exercises in front of men. When the gym