A genetic experiment with peas resulted in one sample of offspring that consisted of 449 green peas and 169 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 yellow?
a. Construct a $95 \%$ confidence interval. Express the percentages in decimal form.
$< \mathrm{p}< \square$ (Round to three decimal places as needed.)
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 yellow?
Yes, the confidence interval does not include 0.25 , so the true percentage could not equal $25 \%$
No, the confidence interval includes 0.25 , so the true percentage could easily equal $25 \%$

Step 1 ：Given that there are 169 yellow peas and a total of 618 peas, we can calculate the sample proportion (\(\hat{p}\)) as the number of yellow peas divided by the total number of peas, which is approximately 0.273.

Step 2 ：We use the z-score for a 95% confidence level, which is approximately 1.96.

Step 3 ：We calculate the standard error (se) using the formula \(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\), which is approximately 0.018.

Step 4 ：We can then construct the 95% confidence interval using the formula \(\hat{p} \pm z \times se\). The lower bound of the confidence interval is approximately 0.238 and the upper bound is approximately 0.309.

Step 5 ：Since the confidence interval does not include 0.25, the results of the experiment appear to contradict the expectation that 25% of the offspring peas would be yellow.

Step 6 ：\(\boxed{\text{Final Answer: Yes, the confidence interval does not include 0.25 , so the true percentage could not equal 25%}}\)