A genetic experiment with peas resulted in one sample of offspring that consisted of 442 green peas and 152 yellow peas. a. Construct a \( 95 \% \) confidence interval to estimate of the percentage of yellow peas. b. Based on the confidence interval, do the results of the experiment appear to contradict the expectation that \( 25 \% \) of the offspring peas would be \( y \) a. Construct a \( 95 \% \) confidence interval. Express the percentages in decimal form. \( \square<\mathrm{p}<\square \) (Round to three decimal places as needed.)

To construct a 95% confidence interval for the percentage of yellow peas, we first need to calculate the sample proportion of yellow peas. The total number of peas is \(442 + 152 = 594\). The proportion of yellow peas (\(p\)) is given by: \[ p = \frac{152}{594} \approx 0.256 \] Next, we calculate the standard error (SE) using the formula: \[ SE = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.256(1 - 0.256)}{594}} \approx 0.020 \] Now, for a 95% confidence interval, we use a z-score of approximately 1.96. The confidence interval is calculated as: \[ \text{CI} = p \pm z \cdot SE \] Calculating this gives us: \[ \text{CI} = 0.256 \pm 1.96 \cdot 0.020 \approx 0.256 \pm 0.039 \] Therefore, the confidence interval for the proportion of yellow peas is: \[ (0.217, 0.295) \] So, expressed in the requested format: \(0.217 < p < 0.295\) (Rounded to three decimal places as needed.) Based on this confidence interval, we can see that the lower bound (0.217) is significantly above the expected percentage of yellow peas (0.25), suggesting that the experimental results do not contradict the expectation. In fact, with this data, we find that there's a considerable chance that yellow peas could represent around 25.6% to 29.5% of the offspring, aligning relatively well with the expectation.