When Mendel conducted his famous genetics experiments with p

When Mendel conducted his famous genetics experiments with peas, one sample of offspring had 152 yellow peas out of 580 peas.

a. construct a 95% confidence interval for the overall proportion of yellow peas.

b. Mendel\'s theory was that 25% of the offspring should be yellow. Since his experiment did not get 25% yellow peas, was he incorrect?

Solution

(a) p=152/580 =0.262069

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) =0.262069 -1.96*sqrt(0.262069*(1-0.262069)/580) =0.2262793

So the upper bound is

p + Z*sqrt(p*(1-p)/n) =0.262069 +1.96*sqrt(0.262069*(1-0.262069)/580) =0.2978587

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(b) No, because there may have some sampling error.