A genetic experiment with peas resulted in one sample of offspring that consiste

Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 406 green peas and 163 yellow peas. Need A and B, please.

A genetic experiment with peas resulted in one sample of offspring that consisted of 406 green peas and 163 yellow peas. a. Construct a 95% confidence interval to estimate of the percentage of yellow peas. bit was expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations? a. Construct a 95% confidence interval. Express the percentages in decimal form

Explanation / Answer

let p=proportion of yellow peas=163/(163+406)=0.2865

here n=569 and var(p)=p(1-p)/n=0.2865*(1-0.2865)/569=0.000359

SE(p)=sqrt(0.000359)=0.0189

(a)(1-alpha)*100% confidence interval for p=p± z(alpha/2)*SE(p)

95% confidence interval for p=p±z(0.05/2)*0.0189=0.2865±1.96*0.0189

=0.2865±0.037=(0.2495,0.3235)

(b) here let x=yellow peas and p=0.25

E(x)=np=0.25*569=142.25

V(x)=np(1-p)=569*0.25*(1-0.25)=106.69

SE(x)=sqrt(106.69)=10.33

we use z-test and z=(x-E(x))/SE(x)=(163-142.25)/10.33=2.0087

the two tailed critical z(0.05)=1.96 is less than 2.0087 so we conclude that % of yellow pea is not 25%.

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