Homework SourseIn an experiment an ebony bodied sepia eyed female was cross
In an experiment, an ebony bodied, sepia eyed female was crossed with a homozygous wild type male. The resulting progeny were allowed to mate with one another. Three repititions of the experiment were conducted. The following data were produced from the crosses. Test these data to determine if they are significantly different from the expected phenotypic ratio. Remember to use the 5% level of significance. Find X2 values for each experiement.
Exp. Wild Ebony Sepia Ebony body
No. Type Body Eye Sepia Eye
1 72 24 20 7
2 112 40 35 11
3 100 31 35 12
Find the X2 value for each experiment. Would pooling of the data be appropriate? If so please calculate and compare the pooled value. If not apporpriate please explain why.
Find Ho ratio, Degrees of freedom, critical value, X2 value and would you reject or not reject the Ho?
Solution
As all results showing 9:3:3:1 ratio, we can pool up the data. It won\'t differ from exact values.
| Null hypothesis | The observed values are not devaiting from 9:3:3:1 ratio | ||||
| Categories | Wild Type | EbonyBody | Sepia Eye | Ebony body, Sepia Eye | Total |
| Observed values | 72 | 24 | 20 | 7 | 123 |
| Expected Ratio | 9 | 3 | 3 | 1 | 16 |
| Expected values | 69.1875 | 23.0625 | 23.0625 | 7.6875 | 123 |
| Deviation | 2.8125 | 0.9375 | -3.0625 | -0.6875 | |
| D^2 | 7.91015625 | 0.87890625 | 9.37890625 | 0.47265625 | |
| D^2/E | 0.114329268 | 0.038109756 | 0.406673442 | 0.06148374 | 0.620596206 |
| X2 value | 0.620596206 | ||||
| DF | 4-1 | 3 | |||
| Inference | The calculated X^2 values is less than table values (7.84 @ 0.05 Probability and 3 DF), hence nullhypothesis accepted. | ||||
| Null hypothesis | The observed values are not devaiting from 9:3:3:1 ratio | ||||
| Categories | Wild Type | EbonyBody | Sepia Eye | Ebony body, Sepia Eye | Total |
| Observed values | 112 | 40 | 35 | 11 | 198 |
| Expected Ratio | 9 | 3 | 3 | 1 | 16 |
| Expected values | 111.375 | 37.125 | 37.125 | 12.375 | 198 |
| Deviation | 0.625 | 2.875 | -2.125 | -1.375 | |
| D^2 | 0.390625 | 8.265625 | 4.515625 | 1.890625 | |
| D^2/E | 0.003507295 | 0.222643098 | 0.121632997 | 0.152777778 | 0.500561167 |
| X2 value | 0.500561167 | ||||
| DF | 4-1 | 3 | |||
| Inference | The calculated X^2 values is less than table values (7.84 @ 0.05 Probability and 3 DF), hence nullhypothesis accepted. | ||||
| Null hypothesis | The observed values are not devaiting from 9:3:3:1 ratio | ||||
| Categories | Wild Type | EbonyBody | Sepia Eye | Ebony body, Sepia Eye | Total |
| Observed values | 100 | 31 | 35 | 12 | 178 |
| Expected Ratio | 9 | 3 | 3 | 1 | 16 |
| Expected values | 100.125 | 33.375 | 33.375 | 11.125 | 178 |
| Deviation | -0.125 | -2.375 | 1.625 | 0.875 | |
| D^2 | 0.015625 | 5.640625 | 2.640625 | 0.765625 | |
| D^2/E | 0.000156055 | 0.169007491 | 0.07911985 | 0.068820225 | 0.31710362 |
| X2 value | 0.31710362 | ||||
| DF | 4-1 | 3 | |||
| Inference | The calculated X^2 values is less than table values (7.84 @ 0.05 Probability and 3 DF), hence nullhypothesis accepted. | ||||
| AFTER DATA POOLING | |||||
| Null hypothesis | The observed values are not devaiting from 9:3:3:1 ratio | ||||
| Categories | Wild Type | EbonyBody | Sepia Eye | Ebony body, Sepia Eye | Total |
| Observed values | 284 | 95 | 90 | 30 | 499 |
| Expected Ratio | 9 | 3 | 3 | 1 | 16 |
| Expected values | 280.6875 | 93.5625 | 93.5625 | 31.1875 | 499 |
| Deviation | 3.3125 | 1.4375 | -3.5625 | -1.1875 | |
| D^2 | 10.97265625 | 2.06640625 | 12.69140625 | 1.41015625 | |
| D^2/E | 0.039092073 | 0.022085838 | 0.135646293 | 0.045215431 | 0.242039635 |
| X2 value | 0.242039635 | ||||
| DF | 4-1 | 3 | |||
| Inference | The calculated X^2 values is less than table values (7.84 @ 0.05 Probability and 3 DF), hence nullhypothesis accepted. |
