Historically, the proportion of all Caucasians in the United States with blood phenotypes A, B, AB and O are 0.41, 0.10, 0.04 and 0.45 respectively. To determine whether current population proportions still match these historical values, a random sample of 200 American Caucasians were selected, and their blood phenotypes were recorded. The observed numbers with each phenotype are given in the following table.
A B AB O
89 18 12 81
Test the hypothesis that the historical values match the current proportions against the alternative that they are not the same. Make sure to write the null hypothesis and alternative formally, show how you construct the test statistic, and state your rejection rule (i.e. justify your choice of).