Question

Consider the following hypothesis tests. (Give your answer bounds exactly.)

(a) Calculate the p-value for H_a: σ² ≠ 18, n = 17, χ² = 27.9.
_____< p < _______

(b) Calculate the p-value for H_a: σ² > 31, n = 30, χ² = 33.
______< p < ______

(c) Calculate the p-value for H_a: σ² ≠ 40, df = 25, χ² = 38.2.
______ < p < ______

(d) Calculate the p-value for H_a: σ² < 14, df = 42, χ² = 26.4.
_____ < p < ______

Answer 1

a)

We have to calculate  p-value for H_a: σ² ≠ 18, n = 17, χ² = 27.9.

here Degree of freedom df will be =n-1=17-1=16

from chi square table at df=16 and

Value of P will be

0.05<P<0.025

b)

We have to Calculate the p-value for H_a: σ² > 31, n = 30, χ² = 33.

here Degree of freedom df will be =n-1=30-1=29

from chi square table at df=29 and

Value of P will be

0.5<P<0.25

c)

We have to Calculate the p-value for H_a: σ² ≠ 40, df = 25, χ² = 38.2.

Degree of freedom is given that is 25

from th chi square table df=25  and

P-value =0.05<0.044<0.01

d)

we have to Calculate the p-value for H_a: σ² < 14, df = 42, χ² = 26.4.

Degree of freedom is given as 42

using the chi square table Value of P will be 0.975<p<0.95