Question

From the given information in each case below, use technology to find the P-value for a chi-square test and give the conclusion for a significance level of α = 0.01. (Use technology to calculate the P-value. Round your answers to three decimal places.)

(a)

χ² = 7.8, df = 2

P-value =

(b)

χ² = 13.1, df = 6

P-value =

(c)

χ² = 17.8, df = 9

P-value =

(d)

χ² = 21.2, df = 4

P-value =

(e)

χ² = 5.4, df = 3

P-value =

Answer 1

Answer 2

SOLUTION :

Using P-value calculator from X^2 value and df : 

https://www.socscistatistics.com/pvalues/chidistribution.aspx

a.

Enter :

X^2 = 7.8

df = 2 

significance level : 0.01

Press calculate :

P-value = 0.020242 = 0.020 approx.   (ANSWER).

As p > 0.01, we do not reject Ho hypothesis. 

b.

Enter :

X^2 = 13.1

df = 6

significance level. : 0.01

Press calculate :

P-value = 0.041475 = 0.041 approx. .  (ANSWER).

As p > 0.01, we do not reject Ho hypothesis. 

c.

Enter :

X^2 = 17.8 

df = 9 

significance level : 0.01

Press calculate :

P-value = 0.037566 = 0.038 approx.   (ANSWER).

As p > 0.01, we do not reject Ho hypothesis. 

d.

Enter :

X^2 = 21.2 

df = 4 

significance level : 0.01

Press calculate :

P-value = 0.000289 = 0.000 approx.   (ANSWER).

As p < 0.01, we  reject Ho hypothesis. 

e.

Enter :

X^2 = 6.4 

df = 3 

significance level : 0.01

Press calculate :

P-value = 0.093691 = 0.094 approx.   (ANSWER).

As p > 0.01, we do not reject Ho hypothesis.