In testing H₀: p $\ge$ .33 versus H_A: p

Question

In testing H₀: p $\ge$ .33 versus H_A: p < .33 with = .20 and n = 100,what is the value of the z-statistic? A)2.77 B)-3.25 C)3.25 D)-2.77

Quizplus · Accepted Answer

First, we need to calculate the standard error of the proportion:
SE = sqrt[(p1q1/n1) + (p2q2/n2)] 
where p1 = 0.33, p2 = 0.20, q1 = 1-0.33 = 0.67, q2 = 1-0.20 = 0.80, n1 = n2 = 100

SE = sqrt[(0.33*0.67/100) + (0.20*0.80/100)] = 0.056

Next, we can calculate the z-statistic:
z = (p1 - p2)/SE

z = (0.33 - 0.20)/0.056 = 2.32 (rounded to two decimal places)

Therefore, the answer is D (-2.77 is not a possible answer, as z should be positive since p1 > p2)

In Testing H0: P ≥\ge≥ 33 Versus HA: P

In Testing H₀: P $\ge$ 33 Versus H_A: P