Answer :
Answer:
The value for the Chi -square test statistics = 1.149
Step-by-step explanation:
The observed value Table can be shown better as:
Observed Value
Age Favorable Unfavorable Neutral Total
18-30 67 24 20 111
30-45 50 14 16 80
Over 45 69 21 26 116
Total 186 59 62 307
NOTE: when computing the question, in the third row and the second column, there is a mistake , the value is supposed to be 21 and not 41 because :
69 +21+ 26 will eventually give = 116
69 + 41 + 26 = 136
With that error being fix , let's get started.
Expected Value
The expected value can be determined by using the formula:
[tex]Expected \ Value = \dfrac{ row \ total \times column \ total }{grand \ total }[/tex]
For 67; (111 * 186)/307 = 67.251
For 24 : (111 * 59)/307 = 21.332
For 20 : (111 * 62)/307 = 22.417
For 50 :(80*186)/307 = 48.469
For 14 : (80* 59)/307 = 15.375
For 16 : ( 0 * 62)/307 = 16.156
For 69 : (116 * 186)/307 = 70.280
For 21 : (116* 59)/307 = 22.293
For 26 : (116*62)/307 = 23.427
Expected Value :
Age Favorable Unfavorable Neutral Total
18-30 67.251 21.332 22.417 111
30-45 48.469 15.375 16.156 80
Over 45 70.280 22.293 23.427 116
Total 186 59 62 307
The Chi - square test statistics = [tex]\dfrac{(observed \ value - Expected \ value)^2}{Expected \ value}[/tex]
For 67.251 : ( 67 - 67.251)²/67.251 = 0.0009
For 21.332 : ( 24 - 21.332)²/21.332 = 0.3337
For 22.417 : ( 20 - 22.417)²/ 22.417 = 0.2606
For 48.469 : ( 50 - 48.469)²/ 48.469 = 0.0484
For 15.375 : ( 14 - 15.375)²/ 15.375 = 0.1230
For 16.156 : ( 16 - 16.156)²/ 16.156 = 0.0015
For 70.280 : ( 69 - 70.280)²/ 70.280 = 0.0233
For 22.293 : ( 21 - 22.293)²/ 22.293 = 0.0750
For 23.427 : ( 26 - 23.427)²/ 23.427 = 0.2826
The chi square table is as follows:
Age Favorable Unfavorable Neutral Total
18-30 0.0009 0.3337 0.2606 0.5952
30-45 0.0484 0.1230 0.0015 0.1729
Over 45 0.0233 0.0750 0.2826 0.3809
Total 0.0726 0.5317 0.5447 1.149
The value for the Chi -square test statistics = 1.149