Given each of the following circumstances determine whether

Given each of the following circumstances, determine whether the calculated values of chi-square are statistically significant:

a.?² = 3.02, df = 1, ? = 0.05

b.?² = 8.09, df = 4, ? = 0.05

c.?² = 10.67, df = 3, ? = 0.01

d.?² = 9.88, df = 2, ? = 0.01

a.?² = 3.02, df = 1, ? = 0.05

Given a=0.05, the critical value of chisquare with 0.95 and df=1 is 3.84 (from chisquare table)

The rejection region is if X^2>3.84, we reject the null hypothesis which is not statistically significant

Since 3.02 is larger than 3.84, we can conclude that values of chi-square are statistically significant

-------------------------------------------------------------------------------------------

b.?² = 8.09, df = 4, ? = 0.05

Given a=0.05, the critical value of chisquare with 0.95 and df=3 is 7.81 (from chisquare table)

The rejection region is if X^2>7.81, we reject the null hypothesis which is not statistically significant

Since 8.09 is larger than 7.81, we can conclude that values of chi-square are statistically significant

-------------------------------------------------------------------------------------------

c.?² = 10.67, df = 3, ? = 0.01

Given a=0.01, the critical value of chisquare with 0.99 and df=3 is 11.34 (from chisquare table)

The rejection region is if X^2>11.34, we reject the null hypothesis which is not statistically significant

Since 10.67 is less than 11.34, we can not conclude that values of chi-square are statistically significant

-------------------------------------------------------------------------------------------

d.?² = 9.88, df = 2, ? = 0.01

Given a=0.01, the critical value of chisquare with 0.99 and df=2 is 9.21 (from chisquare table)

The rejection region is if X^2>9.21, we reject the null hypothesis which is not statistically significant

Since 9.88 is larger than 9.21, we can conclude that values of chi-square are statistically significant