Question

Consider the following hypothesis-testing situations. (Give your answers correct to four decimal places.)

(a) Determine the p-value for H_o: p = 0.5, H_a: p ≠ 0.5, z = 1.4.


(b) Determine the p-value for H_o: p = 0.7, H_a: p ≠ 0.7, z = -2.35.


(c) Determine the p-value for H_o: p = 0.4, H_a: p > 0.4, z = 0.94.


(d) Determine the p-value for H_o: p = 0.2, H_a: p < 0.2, z = -1.5.

Answer 1

Solution :

a) This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

z = 1.4

P(z > 1.4) = 1 - P(z < 1.4) = 1 - 0.9192 = 0.0808

P-value = 2 * P(z > 1.4)

P-value = 2 * 0.0808

P-value = 0.1616

b) This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.7

H_a : p 0.7

z = -2.35

P(z < -2.35) = 0.0094

P-value = 2 * P(z < -2.35)

P-value = 2 * 0.0094

P-value = 0.0188

c) This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.4

H_a : p >  0.4

z = 0.94

P(z > 0.94) = 1 - P(z < 0.94) = 1 - 0.8264 = 0.1736

P-value = 0.1736

d) This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.2

H_a : p < 0.2

z = -1.5

P(z < -1.5) = 0.0668

P-value = 0.0668