Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 413 green peas and 161 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? 

a. Construct a 95% confidence interval. Express the percentages in decimal form.

_______  < p < _______ (Round to three decimal places as needed.) 

b. Given that the percentage of offspring yellow peas is not 25%, do the results contradict expectations?

•  Yes, the confidence interval does not include 0.25, so the true percentage could not equal 25%

•  No, the confidence interval includes 0.25, so the true percentage could easily equal 25%

Answer 1

Gien the no of green peas is 413 and yellow peas is 161in one sample of offspring, hence total sample size is n = 413+161 = 574

a) Now the confidence interal for the proportion of yellow peas is calculated as:

where the sample proportion is calculated as:

and Zc at 95% confidence level is computed using the excel formula for normal distribution which is =NORM.S.INV(0.975), thus the Zc is computed as 1.96

Now the confidence interval is computed as:

Thus the confidence interval for proportion is computed as:

={ 0.24376, 0.31722 }

Converting into percentages we get

={ 24.376% < p < 31.722% }

b) No, the confidence interval includes the 26%/ 25% value so, the true percentage could easily be equal to 25%/ 26%.

Note: he value 25% or 26% in part b is not clearly visible hence i have used both value please answer accordingly.