Supplementary Exercise 9.48 of IPS7e
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Degrees of freedom and P-values for X^2-tests.
Use Table D of PSLS (Table F of IPS) to determine bounds on the P-values.

(a) df = (2-1)*(2-1) = 1; 
P = P(chi^2>1.31) > 0.25 because the 75% percentile is 1.32
(Minitab: P=1-0.747605=0.252)

(a) df = (4-1)*(4-1) = 9; 
P = P(chi^2>17.54) < 0.05 because the 95% percentile is 16.92
(Minitab: P=1-0.959099=0.041)

(a) df = (2-1)*(8-1) = 7; 
P = P(chi^2>22.1) < 0.0025 because the 99.75% percentile is 22.04
(Minitab: P=1-0.997559=0.0024)

(a) df = (5-1)*(3-1) = 8; 
P = P(chi^2>12.61) >0.10 because the 90% percentile is 13.36
(Minitab: P=1-0.874009=0.126)


Minitab commands and listing:

MTB > CDF 1.31;
SUBC>   ChiSquare 1.
Cumulative Distribution Function 

Chi-Square with 1 DF

   x  P( X <= x )
1.31     0.747605

MTB > CDF 17.54;
SUBC>   ChiSquare 9.
Cumulative Distribution Function 

Chi-Square with 9 DF

    x  P( X <= x )
17.54     0.959099

MTB > CDF 22.1;
SUBC>   ChiSquare 7.
Cumulative Distribution Function 

Chi-Square with 7 DF

   x  P( X <= x )
22.1     0.997559

MTB > CDF 12.61;
SUBC>   ChiSquare 8.
Cumulative Distribution Function 

Chi-Square with 8 DF

    x  P( X <= x )
12.61     0.874009