We are working with categorical data, i.e. subscribers and customers and looking at proportions of Citi Bike usage during weekend and weekdays. Therefore Chi-Square test of proportions is implemented in the statistical analysis.The chi square statistic \(\chi^{2\ }\)is given by:
\(\chi^{2\ }=\ \Sigma\frac{\left(f_{observed\ }-\ f_{expected}\right)^2}{f_{expected}}\)
where \(f_{observed\ },\ f_{expected\ }\)
are derived from contingency tables.
\(\)The significance level α is the probability of rejecting the null hypothesis when it is assumed to be true. Let us set α = 0.05, which indicates a 5% risk of concluding that a difference exists when there is no actual difference.\cite{statistics}
Since we use the numeric output, i.e. Chi-square statistic, we compare the P-value to critical value determined by α to make conclusions. For the Chi-square distribution, the critical value at α = 0.05 equals 3.84. \cite{httpinterscissucieduwikiimages33anormal01jpg}
Calculated Chi-square statistics for two selected months (January and July) in 2016 is significantly higher than the critical value. Therefore we can reject \(H_0\) in favor of the \(H_1.\)