Question

From the given information in each case below, state what you know about the P-value for a chi-square test and give the conclusion for a significance level of α = 0.01. Use Table 8 in Appendix A. (Enter your answers to three decimal places.)

(a)    χ² = 4.97, df = 2
< P-value <

Conclusion:

Reject H₀Fail to reject H₀    

(b)    χ² = 12.16, df = 6
< P-value <

Conclusion:

Reject H₀Fail to reject H₀    

(c)    χ² = 20.91, df = 9
< P-value <

Conclusion:

Reject H₀Fail to reject H₀    

(d)    χ² = 18.73, df = 4
P-value  ? > = <

Conclusion:

Reject H₀Fail to reject H₀    

(e)    χ² = 6.24, df = 3
P-value  ? > < =

Conclusion:

Reject H₀Fail to reject H₀    

Answer 1

Solution:

We have to use here the chi-square table to find the upper and lower limit of the p-value. The decision rule is if the p-value is less than the significance level, we reject H0 else we fail to reject.

(a)    χ² = 4.97, df = 2

Answer:

Conclusion:

Fail to reject H₀

(b)    χ² = 12.16, df = 6

Answer:

Conclusion:

Fail to reject H₀

(c)    χ² = 20.91, df = 9

Answer:

Conclusion:

Fail to reject H₀

(d)    χ² = 18.73, df = 4

Answer:

Conclusion:

Reject H₀

(e)    χ² = 6.24, df = 3

Answer:

Conclusion:

Fail to reject H₀