Question

ion 10.2: Survey Results. Assume that a yes/ sample of female and male subjects and the results are summarized in a two-way the one to the right. Use the given value of the y2 test statistic and the given signinica level to test for independence between gender and response, consulting table needed. [1 point each no survey question is presented to a simple random table li ke 10.7 as Yes No Male Female 3) Test statistic: χ2 = 7.82; significance level-01 4) Test statistic:x2-2.96; significance level-.05

Answer 1

Solution:

We are given that 2 by 2 table.

Thus

df = degrees of freedom = ( m - 1) X ( n-1 ) = (2-1) X( 2-1) = 1 X 1 = 1

Part 3) Given: Test statistic = $\chi^{2}=7.82$

Significance level = 0.01

Thus look in Chi-square table for df = 1 and Right tail area = 0.01 and find Chi-square critical value.

X.900 010 6.635 9.210 3 0.072 0.1150.216 0.352 0.584 6.251 7.815 9.348 11.345 4 0.207 0.2970.484 0.711 1.0647.779 9.488 11.143 13.277 3.841 5.991 2 0.010 0.020 4.605 7.378 9 0.831 0.676 7 0.989 8 1.344 1.1451.610 9.236 11.070 12.83315.086 1.635 2.167 1.239 1.6462.180 2.088 2.700 3.325 1.237 1.6 1.690 2.20410.645 12.592 14.44916.812 2.83312.017 14.067 16.01318.475 3.490 13.362 15.507 17.535 20.090 4.168 14.684 16.919 19.02321.666 10 2.156 3.247 4.865 15.987 18.307 20.483 23.209

Thus Chi-square critical value for 0.01 significance level = 6.635

Since Test statistic = $\chi^{2}=7.82$ > Chi-square critical value = 6.635, we reject null hypothesis H0: Gender and response are independent.

Thus we conclude that: Gender and response are not independent or in other words Gender and response are dependent.

Part 4) Test statistic = $\chi^{2}=2.96$

Chi-square critical value for 0.05 significance level = 3.841

Since Test statistic = $\chi^{2}=2.96$ < Chi-square critical value = 3.841, we failed to reject H0

and thus we conclude that : Gender and response are independent.