In genetic studies of maize (Zea mays), kernel color (purple vs. yellow) and kernel shape (smooth vs. wrinkled) are inherited independently. A dihybrid cross between two heterozygous plants is expected to produce offspring with a phenotypic ratio of 9 purple-smooth : 3 purple-wrinkled : 3 yellow-smooth : 1 yellow-wrinkled.
A student harvested a total of 160 kernels from one cob resulting from this cross.
The student performed a chi-squared (χ2\chi^2χ2) test on the phenotypes of the 160 kernels. Part of the calculation is shown in the table below.
| Phenotypes | Observed number (OOO) | Expected number (EEE) | O−EO-EO−E | (O−E)2(O-E)^2(O−E)2 | (O−E)2E\frac{(O-E)^2}{E}E(O−E)2 |
|---|---|---|---|---|---|
| Purple, smooth | -9.0 | 81.0 | 0.90 | ||
| Purple, wrinkled | 3.0 | 9.0 | 0.30 | ||
| Yellow, smooth | 3.0 | 9.0 | 0.30 | ||
| Yellow, wrinkled | 3.0 | 9.0 | 0.90 | ||
| χ2=\chi^2 =χ2= | 2.40 |
Complete the table by finding the value of the observed (OOO) and expected (EEE) numbers for each phenotype.
Using the portion of the χ2\chi^2χ2 critical values table below, identify the critical value for this test at the 5%5\%5% significance level (p=0.05p = 0.05p=0.05).
| Degrees of freedom (ν\nuν) | 10%10\%10% level (p=0.10p=0.10p=0.10) | 5%5\%5% level (p=0.05p=0.05p=0.05) | 1%1\%1% level (p=0.01p=0.01p=0.01) |
|---|---|---|---|
| 1 | 2.706 | 3.841 | 6.635 |
| 2 | 4.605 | 5.991 | 9.210 |
| 3 | 6.251 | 7.815 | 11.340 |
| 4 | 7.779 | 9.488 | 13.277 |
State whether the student should accept or reject the null hypothesis (that there is no significant difference between the observed and expected ratios), and justify your answer using the calculated χ2\chi^2χ2 value and the critical value.
