We conduct a significance test with H0: p = 0.43 and Ha: p × 0.43. We take a sample of size 250 and get a sample proportion of 0.40. The appropriate test statistic is:
A) $ z=0.43 \pm 1.96 \sqrt{\frac{0.43-0.57}{230}} $

B) $ z=\frac{0.40-0.43}{\sqrt{\frac{0.43 \cdot 0.57}{250}}} $

C) $ z=0.40 \pm 1.96 \sqrt{\frac{0.40 \cdot 0.60}{250}} $

D) $ z=\frac{0.40-0.43}{\sqrt{\frac{0.40-0.60}{250}}} $

E) $ z=\frac{0.43-0.40}{\sqrt{\frac{0.40-0.60}{250}}} $

Question

We conduct a significance test with H0: p = 0.43 and Ha: p × 0.43. We take a sample of size 250 and get a sample proportion of 0.40. The appropriate test statistic is: 
A) $ z=0.43 \pm 1.96 \sqrt{\frac{0.43-0.57}{230}} $

B) $ z=\frac{0.40-0.43}{\sqrt{\frac{0.43 \cdot 0.57}{250}}} $

C) $ z=0.40 \pm 1.96 \sqrt{\frac{0.40 \cdot 0.60}{250}} $

D) $ z=\frac{0.40-0.43}{\sqrt{\frac{0.40-0.60}{250}}} $

E) $ z=\frac{0.43-0.40}{\sqrt{\frac{0.40-0.60}{250}}} $

Quizplus · Accepted Answer

We are testing the null hypothesis that p = 0.43 (note that there is a typo in the alternative hypothesis where it should say "p ≠ 0.43" instead of "p × 0.43"). Since we have a sample proportion of 0.40, we can use the standard normal distribution to calculate the test statistic:

z = (p̂ - p) / sqrt(p(1-p)/n)
z = (0.40 - 0.43) / sqrt(0.43*0.57/250)
z = -1.123

The appropriate test statistic is therefore B) z=(0.40−0.43)/sqrt((0.43cdot0.57)/250)

We Conduct a Significance Test with H0: P = 0 z=0.43±1.960.43−0.57230 z=0.43 \pm 1.96 \sqrt{\frac{0.43-0.57}{230}} z=0.43±1.962300.43−0.57​​

We Conduct a Significance Test with H0: P = 0 $z=0.43 \pm 1.96 \sqrt{\frac{0.43-0.57}{230}}$