When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 155 yellow peas for a total of 583 peas. a) Find a 95% confidence interval estimate of the percentage of yellow peas and then interpret your answer.

Accepted Solution

Answer:(0.23, 0.30)Step-by-step explanation:Number of green peas = 428Number of yellow peas = 155Total number of peas = n = 583Since we have to establish the confidence interval for yellow peas, the sample proportion of yellow peas would be considered as success i.e. p = [tex]\frac{155}{583}[/tex]q = 1 - p = [tex]\frac{428}{583}[/tex]Confidence Level = 95%Z value associated with this confidence level = z = 1.96Confidence interval for the population proportion is calculated as:[tex](p-z\sqrt{\frac{pq}{n}} ,p+z\sqrt{\frac{pq}{n}})[/tex]Using the values, we get:[tex](\frac{155}{583}-1.96\sqrt{\frac{\frac{155}{583} \times\frac{428}{583}}{583} },\frac{155}{583}+1.96\sqrt{\frac{\frac{155}{583} \times\frac{428}{583}}{583} })\\\\ =(0.23,0.30)[/tex]Conclusion:We are 95% confident that true value of population proportion of yellow peas lie between 0.23 and 0.30