Analysis of Gender Preferences in Gym Membership

STATISTICS
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Section 1
(a) Pivot table to represent the female customers that want unisex gym is highlighted below.
(b) Relationship between the minutes on cardio and minutes on weight machine is
represented through scatter plot.
The scatter plot represent negative slope which indicates that higher spending on cardio by
male/female would decrease the time spent on the weight machine. This is because the total time
of exercise is usually fixed and it is divided between weight training and cardio. Therefore, if a
higher time is spent on cardio, then lower time is spent on weight machine and vice versa (Flick,
2015).
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(c) Pivot table to represent the customers that want or do not want unisex gym is highlighted
below.
It can be said based on the above that 64.86% of female prefer unisex gym while 35.14% male
prefer unisex gym. Further, 64.86% - 35.14 % = 29.72% more female would prefer to go unisex
gym.
(d) Pivot table to represent the relationship between the time spent on cardio machine with
the gender of customer.
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Females are spending a mean of 36.48 minutes ion cardio while males are spending only 15
minutes on cardio. Hence, females would spend 36.48 minutes – 15 minutes = 21.48 minutes
more on an average on cardio machine.
Section 2
(a) 90% confidence interval for the sample proportion of female who will say yes to Unisex
gym
For female customers
Total female customers in sample n=44
Number of female who would prefer unisex gym = 24
Sample proportion of female who would prefer unisex gym ^p= 24
44 =0.545
Standard error of sample proportion ¿ √ ^p ¿¿ ¿
The z value of 90% confidence interval = 1.645
Lower limit 90% confidence
¿ Sample proportion− ( z value∗d error )=0.545− (1.645∗0.075 )=0.4220
Upper limit 90% confidence
¿ Sample proportion+ ( z value∗d error ) =0.545+ ( 1.645∗0.075 ) =0.6689
Thus, 90% confidence interval would be [0.4220 0.6689]
(b) 90% confidence interval for the sample proportion of male who will say yes to Unisex
gym
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