Question

Please be clear and explain! Thanks!

9-­‐7: A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H0: μ=12 against H1: μ<12, using a random sample of four specimens. Find the boundary of the critical region if the type I error probability is: a) α=0.01 and n=4 b) α=0.05 and n=4 c) α=0.01 and n=16 d) α=0.05 and n=4

Answer 1

Solution:-

H₀: μ = 12 against H₁: μ < 12,

This is left tailed test.

a) The boundary of the critical region is Boundary is (- infinity, -4.541).

Type I error probability is 0.01.

n = 4

D.F= 3

t_critical = - 4.541

Boundary is (- infinity, -4.541)

b)The boundary of the critical region is Boundary is (- infinity, - 2.354).

Type I error probability is 0.05

n = 4

D.F= 3

t_critical = - 2.354

Boundary is (- infinity, - 2.354)

c)

The boundary of the critical region is Boundary is (- infinity, - 2.602).

Type I error probability is 0.01

n = 16

D.F= 15

t_critical = - 2.602

Boundary is (- infinity, - 2.602)

d) The boundary of the critical region is Boundary is (- infinity, - 2.354).

Type I error probability is 0.05

n = 4

D.F= 3

t_critical = - 2.354

Boundary is (- infinity, - 2.354)