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.

Step-by-step explanation

Confidence level = 90% = 0.90

number of successes = 155

sample size = 414 + 155 = 569

so ,

`\hat{p}=(x)/(n)=(155)/(569)\approx0.2724`

for confidence level ,

`1-\alpha=1-0.90=0.10`

so ,

`z_{(\alpha)/(2)}=1.645`

margin of error =

`\begin{gathered} E=z_{(\alpha)/(2)}(\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}) \\ \\ E=1.645*\sqrt{(0.2724(1-0.2724))/(569)} \\ \\ E=1.645*√(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