Question

4. When Mendel conducted his famous genetics experiments using peas, one sample of offspring consisted of 152 yellow peas out of the total 580 plants. Use a 0.1 significance level to test his claim that 25% of offspring peas will be yellow. Find the 90% confidence interval of the population proportion and compare your results.

Answer 1

sample proportion, = 0.2621
sample size, n = 580
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.2621 * (1 - 0.2621)/580) = 0.0183

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.0183
ME = 0.03

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.2621 - 1.64 * 0.0183 , 0.2621 + 1.64 * 0.0183)
CI = (0.232 , 0.292)

As the confidence interval contains 25% fail to reject the null hypothesis