Question

a genetic experiment with peas resulted in one sample of offspring that consisted of 418 green peas and 151 yellow peas. a.) construct a 95% confidence interval to estimate the percentage of yellow peas. b.) interpret this interval

Answer 1

Answer:

95% Confidence interval:  (0.2291,0.3015)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 418+151 = 569

Number of yellow peas, x = 151

$\hat{p} = \dfrac{x}{n} = \dfrac{151}{569} = 0.2653$

a) 95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.2653\pm 1.96(\sqrt{\dfrac{0.2653(1-0.2653)}{569}}) = 0.2653\pm 0.0362\\\\=(0.2291,0.3015)$

b) Interpretation of confidence interval

We are 95% confident that the proportion of yellow peas in the sample lies within the range (0.2291,0.3015)