Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 413 green peas and 159 yellow peas. a. Construct a 90?% confidence interval to estimate of the percentage of yellow peas. b. It 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?

Answer 1

Sol:

total=413+159=572

proportio of yellow peas=p^=x/n=159/572=0.277972

Z crit for 90%=1.645

90?% confidence interval to estimate of the percentage of yellow peas

p^-z*sqrt(p^(1-p^)/n,p^+z*sqrt(p^(1-p^)/n

0.277972-1.645sqrt(0.277972*(1-0.277972)/572),0.277972+1.645sqrt(0.277972*(1-0.277972)/572)

0.2472,0.3088

lower limit=0.2472=24.72%

upper limit=0.3088=30.88%

we are 90% confident that the true popualtion percentage of yellow peas lies in between 24.72% and 30.88%

results do not contradict? expectations it supports contracdiction that  It was expected that? 25% of the offspring peas would be yellow

as 25% is in the confidence interval range of 24.72% and 30.88%

24.72%<25%<30.88%