Business Statistics: Summary, Hypothesis Testing, and Conclusion

Business Statistics
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“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 “
gender Female
Row Labels Count of Should the gym be Unisex?
no 27
yes 28
Grand Total 55
The sample proportion that say yes is;
^p= number of cases
Total number = 28
55 =0.5091
The calculation clearly shows that the percentage of the female participants who want a unisex gym
is 50.91% (Morey, Hoekstra, Rouder, Lee, & Wagenmakers, 2016).
“ 1b) Summary of the relationship between the variables ‘time on cardio machine’ and ‘time on
weight machine’ “

The above scatter clearly indicates that there is a positive linear relationship between minutes on
Cardio and minutes on weight machine.
“1c) Summary that lets you investigate the relationship between the variable ‘does the customer
want a unisex gym’ and ‘gender’ “
Count of Should the gym be Unisex? Column Labels
Row Labels no yes
Grand
Total
Female 27 28 55
Male 35 10 45
Grand Total 62 38 100
Count of Should the gym be Unisex? Column Labels
Row Labels no yes
Grand
Total
Female 49.09% 50.91% 100.00%
Male 77.78% 22.22% 100.00%
Grand Total 62.00% 38.00% 100.00%
The above tables shows that a large percentage of the female participants would desire to have a
unisex gym when compared to the male participants.
“1d)Summary that lets you investigate the relationship between the variable ‘time spent on the
cardio machine ’ and ‘gender’ “
Row Labels Average of Minutes on Cardio StdDev of Minutes on Cardio
Female 37.364 17.661
Male 17.000 16.563
Grand Total 28.200 19.893

Female participants were on average found to spend more time on Cardio machine as compared to
the male participants. As can be seen, females on average spent 37.36 (SD = 17.66) while males on
average spent 17.00 (SD = 16.56).
“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”
90% confidence interval for sample proportion for females
Count of Should the gym be Unisex? Column Labels
Row Labels no yes
Grand
Total
Female 27 28 55
Male 35 10 45
Grand Total 62 38 100
Considering females only, we have;
N = 55,
Sample proportion ^p= number of cases
Total number = 28
55 =0.5091
Standard error of sample proportion = √ 0.5091(1−0.5091)
55 = √ 0.004544=0.067409
90% confident the true proportion is between
0.5091 ±1.645∗0.067409=0.5091 ±0.110888
Lower limit: 0.5091−0.110888=0.398212
Upper limit: 0.5091+0.110888=0.619988
“2b) Calculation of confidence interval for the proportion of males that prefer a Unisex gym using
my allocated sample”