Question

1. A test of the null hypothesis *H*_{0}:
*μ* = *μ*_{0} 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* >
*μ*_{0}?

(b)What is the *P*-value if the alternative is
*H*_{a}: *μ* <
*μ*_{0}?

(c)What is the *P*-value if the alternative is
*H*_{a}: *μ* ≠
*μ*_{0}?

2. A test of the null hypothesis *H*_{0}:
*μ* = *μ*_{0} gives test statistic *z*
= −1.65.

(a) What is the *P*-value if the alternative is
*H*_{a}: *μ* >
*μ*_{0}?

(b) What is the *P*-value if the alternative is
*H*_{a}: *μ* <
*μ*_{0}?

(c) What is the *P*-value if the alternative is
*H*_{a}: *μ* ≠
*μ*_{0}?

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**

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