Question

A genetic experiment with peas resulted in one sample of all springs that consisted of 414 green peas

Answer 1

Given

Confidence level = 90% = 0.90

green peas = 414

yellow peas = 155

Find

Estimate of the percentage of yellow peas.

Explanation

Confidence level = 90% = 0.90

number of successes = 155

sample size = 414 + 155 = 569

so ,

$\hat{p}=\frac{x}{n}=\frac{155}{569}\approx0.2724$

for confidence level ,

$1-\alpha=1-0.90=0.10$

so ,

$z_{\frac{\alpha}{2}}=1.645$

margin of error =

$\begin{gathered} E=z_{\frac{\alpha}{2}}(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}) \\ \\ E=1.645\times\sqrt{\frac{0.2724(1-0.2724)}{569}} \\ \\ E=1.645\times\sqrt{0.00034832731} \\ \\ E=0.03070150499\approx0.0307 \end{gathered}$

boundaries of the confidence level are

$\begin{gathered} \hat{p}-E=0.2724-0.0307=0.2417=24.17\% \\ \hat{p}-E=0.2724+0.0307=0.3031=30.31\% \end{gathered}$

Final Answer

Hence , the estimate of the percentage of yellow peas is between 0.242 and 0.303