Objective 50a A certain plant when self-pollinated produced 400 offspring, 317 of which had white flowers and 83 of which had colored flowers. Demonstrate through the use of Chi-square whether this segregation fits better a ratio of 3:1 or 13:3. Explain
null hypothesis:Ho: there is a 3:1 ratio of white to colored flower.
alternate hypothesis:Ha: ratio of white to colored flower. is different from 3:!.
degree of freedom =categories-1= | 1 |
for 0.05 level and 1 degree of freedom :rejection region = | 3.841 |
applying chi square goodness of fit test:
observed | Expected | Chi square | |||
category | Probability(p) | O_{i} | E_{i}=total*p | R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} | |
white | 0.750 | 317.000 | 300.000 | 0.963 | |
colored | 0.250 | 83.000 | 100.000 | 2.890 | |
total | 1.000 | 400 | 400 | 3.853 |
Decision:as test statitic 3.853 is in rejection region we reject null hypothesis
Conclusion: we have sufficient evidence at 5% level to conclude that there is a significant difference in proprotion of white to colored flowers from 3:1.
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