Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 418 green peas and 163 yellow peas. a. Construct a 95​% 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 of yellow peas = 163 / (418 + 163) = 163 / 581 = 0.281

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n] < p < + Z/2 * sqrt [ ( 1 - ) / n]

0.281 - 1.96 * sqrt [ 0.281 ( 1 - 0.281) / 581] < p < 0.281 + 1.96 * sqrt [ 0.281 ( 1 - 0.281) / 581]

0.244 < p < 0.318

95% CI is ( 0.244 , 0.318 )

Since 0.25 contained in confidence interval, it is possible that percentage of offspring yellow peas is easily 25%