Question

a genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 161 yellow peas.
a. construct a 90% 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 90% confidence interval. express the percentages in decimal form.
□ < p < □ (round to three decimal places as needed.)

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}$ is calculated as $\hat{p}=\frac{x}{n}$, where $x$ is the number of yellow peas and $n$ is the total number of peas. Here, $x = 161$ and $n=434 + 161=595$. So, $\hat{p}=\frac{161}{595}\approx0.271$.

Step2: Find critical value

For a 90% confidence interval, the significance level $\alpha=1 - 0.90 = 0.10$, and $\alpha/2=0.05$. The critical value $z_{\alpha/2}$ from the standard normal distribution table is $z_{0.05}\approx1.645$.

Step3: Calculate margin of error

The margin of error $E$ is given by the formula $E = z_{\alpha/2}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$. Substitute $\hat{p}=0.271$, $n = 595$, and $z_{\alpha/2}=1.645$ into the formula:

$$
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Step4: Construct confidence interval

The confidence interval is $\hat{p}-E$0.271- 0.030

Answer:

$0.241