Final answer:
To find the 99% confidence interval estimate of the percentage of green peas, we use the formula CI = p ± Z * sqrt(p * (1-p) / n). The confidence interval is approximately 0.698 to 0.777, or 69.8% to 77.7%. The observed value of 73.8% falls within this interval, indicating that the results do not significantly contradict Mendel's theory.
Step-by-step explanation:
To find the 99% confidence interval estimate of the percentage of green peas, we can use the formula:
CI = p ± Z * sqrt(p * (1-p) / n)
Where p is the observed proportion of green peas, Z is the Z-score for the desired level of confidence, and n is the sample size. In this case, p = 428/580 = 0.7379, Z = 2.576 for a 99% confidence level (standard normal distribution), and n = 580. Plugging these values into the formula, we get a confidence interval of approximately 0.698 to 0.777, or 69.8% to 77.7%. To determine if the results contradict Mendel's theory, we compare the expected percentage of green peas (75%) with the observed percentage (73.8%). Since the observed value of 73.8% falls within the confidence interval of 69.8% to 77.7%, we can conclude that the results do not significantly contradict Mendel's theory. However, it is worth noting that the observed percentage is slightly lower than expected, indicating some deviation from the predicted value.