Final answer:
Using a Chi-square test on the observed 141 white, 291 pink, and 132 red pea flowers against the expected Mendelian 1:2:1 ratio, the calculated chi-square value is lower than the critical value at the 5 percent significance level. This means there is no significant deviation from the expected ratios, supporting Mendel's genetic theory.
Step-by-step explanation:
According to Mendelian genetics, a sample of 564 pea plants resulted in 141 white, 291 pink, and 132 red flowers. We will use a Chi-square test to determine if these observed frequencies significantly deviate from the expected ratios at the 5 percent level of significance.
Assuming that the ratios should follow Mendel's expected 1:2:1 ratio (since we have three phenotypes, which suggest incomplete dominance), we would expect (564/4) = 141 plants of each the white and red (the homozygous conditions) and (564/2) = 282 of the pink (the heterozygous condition). Our observed values are 141 white, 291 pink, and 132 red flowers.
The Chi-square formula is:
Χ² = Σ[(O-E)²/E]
where O = observed frequency, E = expected frequency.
Calculating for each category:
- White: (141-141)²/141 = 0
- Pink: (291-282)²/282 ≈ 0.287
- Red: (132-141)²/141 ≈ 0.57
Summing these values gives us a Χ² score of approximately 0.857. The degrees of freedom (df) for this test is the number of phenotypic categories minus 1, which in this case is 2 (df = 3-1).
Looking up the critical value of Χ² at 2 df and 5% significance level, we find it to be 5.99. Since our calculated Χ² score of approximately 0.857 is less than 5.99, we cannot reject the null hypothesis, and it can be concluded that there is no significant difference between the observed and expected ratios of flower colors. Therefore, the result supports Mendel's theory.