Question

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

(a) Calculate the p-value for H_a: σ² ≠ 21, n = 29, χ² = 28.7.
< p <  

(b) Calculate the p-value for H_a: σ² > 28, n = 10, χ² = 32.9.
< p <  

(c) Calculate the p-value for H_a: σ² ≠ 41, df = 22, χ² = 38.2.
< p <  

(d) Calculate the p-value for H_a: σ² < 10, df = 43, χ² = 25.5.

Answer 1

SOLUTION:

From given data,

(a) Calculate the p-value for H_a: σ² ≠ 21, n = 29, χ² = 28.7.

χ² = 28.7. (two - tailed)

n = 29,

degree of freedom= n-1 = 29-1 = 28

p- value = 0.42785986

(b) Calculate the p-value for H_a: σ² > 28, n = 10, χ² = 32.9.

χ² = 32.9 (right - tailed)

n = 10,

degree of freedom= n-1 = 10-1 = 9

p- value =0.00013901

0 < p < 0.00013901

(c) Calculate the p-value for H_a: σ² ≠ 41, df = 22, χ² = 38.2.

χ² = 38.2 (two - tailed)

degree of freedom= 22

p- value =0.01739732

-0.01739732 < p < 0.01739732

(d) Calculate the p-value for H_a: σ² < 10, df = 43, χ² = 25.5.

χ² = 25.5 left - tailed)

degree of freedom= 43

p- value =0.98438891

-0.98438891 < p < 0.98438891