Given here are the observed sample proportions p̂ in the contexts of parts (a-d.) of Exercise 8.62. Calculate the test statistic and draw a conclusion of the test at the specified level of significance.
(a) p̂ = .233
(b) p̂ = .72
(c) p̂ = .54
(d) Claim p̂ = .86

Data from in Exercise 8.62

Each part of this problem specifies a claim about a population proport ion, the sample size n, and the desired level of significance a. Formulate (i) the hypotheses, (ii) the test statistic, and (iii) the rejection region. (The answers to p art (a) are provided for illustration.)

Claim p < .32   n = 120   a = .05