To help understand how the value of the chi-square statistic is related to departures from expected proportions, it is useful to use a statistical package to compare a sample of contrived data to the expected proportions for a population. Use expected proportions of 1:1 (e.g. male and females) and a sample size of 100.
(a) Initially, set the observed numbers in each category as 50:50 and run a single sample chi-square test. What would you expect the value of chi-square to be?
(b) Now, change the sample numbers to 45 and 55 and rerun the test. Repeat this for increasing departures from the expected ratio (e.g. 40 and 60, 35 and 65, 30 and 70). What happens to the value of chisquare? What happens to the probability?