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 = 1.59.


(b) Determine the p-value for H_o: p = 0.7, H_a: p ≠ 0.7, z = -2.32.


(c) Determine the p-value for H_o: p = 0.4, H_a: p > 0.4, z = 1.02.


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

Answer 1

a) Given that, the null and alternative hypotheses are,

H0 : p = 0.5

Ha : p ≠ 0.5

Test statistic is, Z = 1.59

p-value = 2 * P(Z > 1.59) = 2 * 0.0559 = 0.1118

=> p-value = 0.1118

b) Given that, the null and alternative hypotheses are,

H0 : p = 0.7

Ha : p ≠ 0.7

Test statistic is, Z = -2.32

p-value = 2 * P(Z < -2.32) = 2 * 0.0102 = 0.0204

=> p-value = 0.0204

c) Given that, the null and alternative hypotheses are,

H0 : p = 0.4

Ha : p > 0.4

Test statistic is, Z = 1.02

p-value = P(Z > 1.02)= 1 - P(Z < 1.02) = 1 - 0.8461 = 0.1539

=> p-value = 0.1539

d) Given that, the null and alternative hypotheses are,

H0 : p = 0.2

Ha : p < 0.2

Test statistic is, Z = -1.5

p-value = P(Z < -1.5) = 0.0668

=> p-value = 0.0668