Question

 A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 151 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

Total number of peas = 434 + 151 = 585

Proportion of yellow peas ( $\hat{p}$ ) = 151/585 = 0.2581 and 1 - $\hat{p}$ = 0.7419

Zcritical at $\alpha$ = 0.05 (2 tailed) = 1.96

The Confidence interval = $\hat{p}$ $\pm$ ME

where ME = Zcritical * SQRT[( $\hat{p}$ (1 - $\hat{p}$ )/n] = 1.96 * Sqrt(0.2581*0.7419/585) = 0.0355

The Lower limit = 0.2581 - 0.0355 = 0.2226 $\approx$ 0.223

The Upper Limit = 0.2581 + 0.0355 = 0.2936 $\approx$ 0.294

The 95% confidence interval for yellow peas 0.223 < p < 0.294

If it is given that the % of offspring is not 25%, then NO, it does not contradic expectattions as the confidence interval contains the value of 25%.