State whether the following statements are true or false and explain why.
(a) It is more difficult to estimate a population proportion precisely if its value is near 0.50.
(b) A χ2 goodness-of-fit test has the null hypothesis that category proportions are all equal.
(c) A χ2 goodness-of-fit test is used for observational studies whereas a χ2 test of independence is used for experiments.
(d) χ2s = 0 when the observed data are in perfect agreement with the null hypothesis.