Question

1. A test of the null hypothesis H₀: μ = μ₀ gives test statistic z = 0.26. (Round your answers to four decimal places.

(a) What is the P-value if the alternative is H_a: μ > μ₀?

(b)What is the P-value if the alternative is H_a: μ < μ₀?

(c)What is the P-value if the alternative is H_a: μ ≠ μ₀?

2. A test of the null hypothesis H₀: μ = μ₀ gives test statistic z = −1.65.

(a) What is the P-value if the alternative is H_a: μ > μ₀?

(b) What is the P-value if the alternative is H_a: μ < μ₀?

(c) What is the P-value if the alternative is H_a: μ ≠ μ₀?

Answer 1

1)

a)

z = 0.26

For right tailed test, Ha: > 0.

p-value = P( Z > z)

= P( Z > 0.26)

= 1 - P( Z < 0.26)

= 1 - 0.6026

= 0.3974

b)

For left tailed test H0: < 0

p-value = P( Z < z)

= P( Z < 0.26)

= 0.6026

c)

For two tailed test, H0: 0

p-value = 2 * P( Z > z)

= 2 * 0.3974

= 0.7948

2)

a)

For right tailed test, Ha: > 0.

p-value = P( Z > z)

= P( Z > -1.65)

= P( Z < 1.65)

= 0.9505

b)

For left tailed test H0: < 0

p-value = P( Z < z)

= P( Z < -1.65)

= ( 1 - P( Z < 1.65) )

= 1 - 0.9505

= 0.0495

c)

For two tailed test, H0: 0

p-value = 2 * P( Z < z)

= 2 * 0.0495

= 0.0990