A medical researcher wants to test if the proportion of people who frequently have headaches is different between coffee drinkers and non$-$coffee drinkers. Two independent random samples are collected, one of coffee drinkers and one of non$-$coffee drinkers. The researchers recorded whether each person has headaches frequently. A chi$-$square test of homogeneity is used to test the hypothesis and the $\backslash$chi $2$ test statistic is calculated to be $4\mathrm{.}5.$ Suppose the researcher decides to analyze the data using a two$-$proportion z$-$test instead, what would be the absolute value of the z$-$test statistic?