Question

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

(a) Calculate the p-value for H_a: σ² ≠ 22, n = 16, χ² = 28.2.
_______< p <_______

(b) Calculate the p-value for H_a: σ² > 28, n = 26, χ² = 32.6.
_______< p <________

(c) Calculate the p-value for H_a: σ² ≠ 44, df = 30, χ² = 39.
_______< p < _______

(d) Calculate the p-value for H_a: σ² < 13, df = 40, χ² = 26.5.
_______< p < ________

Answer 1

The P-value for chi-squared test is calculated using chi-square table or by the calculator, the table is shown below:

hence

(a). The p-value for H_a: σ² ≠ 22, n = 16, χ² = 28.2

0.01<P<0.05

(b) The p-value for H_a: σ² > 28, n = 26, χ² = 32.6

0.10<P<0.20

(c) The p-value for H_a: σ² ≠ 44, df = 30, χ² = 39

0.10<P<0.20

(d) The p-value for H_a: σ² < 13, df = 40, χ² = 26.5

0.90<P<0.95

all the values are calculated using calculatar and also by comparing with above table