Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 438 green peas and 169 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

sample proportion, = 0.2784
sample size, n = 607
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2784 * (1 - 0.2784)/607) = 0.0182

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.645

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2784 - 1.645 * 0.0182 , 0.2784 + 1.645 * 0.0182)
CI = (0.2485 , 0.3083)

24.85% and 30.83%

From the calculated CI, we can conclude that the percetage is 25%.

However in actual is not 25%, this contracticts.