Answer to Question #345315 in Statistics and Probability for Rhea

Question

Activity 2

Find the rejection region for each hypothesis test based on the information given.

1 H₂ μ = 121

Hah > 121 Η μ=986

2. Ho:μ=986 Ị Hai =27

HaiH <27

a= 0.01

a= 0.05 a= 0.05

n=34

known unknown

n=25 n=12

a known

Answer 1

1.

$H_0: \mu=121$

$H_a:\mu>121$

$\sigma$ known, $n=34, \alpha=0.01$

This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

$$z\ge2.3263$$

2.

$H_0: \mu=986$

$H_a:\mu\not=986$

$\sigma$ unknown, $n=25, \alpha=0.5$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

$df=n-1=24$ degrees of freedom

$$|t|\ge2.0639$$

3.

$H_0: \mu=27$

$H_a:\mu<27$

$\sigma$ known, $n=12, \alpha=0.05$

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

$$z≤-1.6449$$