Question

My question is on a practice textbook problem - and generally when comparing proportions and you get a negative test statistic. Why is this compared to the –ve critical value.

For example in the scenario below. The textbook answer says Reject H₀ since −2.86 < −2.58, p = .0042

Using R, the p-value is less than 0.05 so I would reject H₀ . However, calculating by hand,  normally I would compare the test statistic to a critical value of 2.58 and not -2.58. If I do this I would have to fail to reject the null. Which is incorrect. Please explain why I am comparing to the negative critical value in the question below

Question 7.6.1: Ho et al. (A-22) used telephone interviews of randomly selected respondents in Hong Kong to obtain information regarding individuals’ perceptions of health and smoking history. Among 1222 current male smokers, 72 reported that they had “poor” or “very poor” health, while 30 among 282 former male smokers reported that they had “poor” or “very poor” health. Is this sufficient evidence to allow one to conclude that among Hong Kong men there is a difference between current and former smokers with respect to the proportion who perceive themselves as having “poor” and “very poor” health? Let α = .01

Answer 1