Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 441green peas and 166 yellow peas.

a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

__ <P< __

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

SOLUTION:

From given data,

A genetic experiment with peas resulted in one sample of offspring that consisted of 441 green peas and 166 yellow peas.

= 166

n = 441+166 = 607

= / n = 166 / 607 = 0.273

a. Construct a 95​% confidence interval to estimate of the percentage of yellow peas.

95% confidence interval

Confidence interval is 95%

95% = 95/100 = 0.95

= 1 - Confidence interval = 1-0.95 = 0.05

/2 = 0.05 / 2

= 0.025

Z_/2 = Z_0.025 = 1.96

CI of 95%

=    Z_/2 * sqrt( *(1-) / n )

= 0.273   1.96* sqrt(0.273 *(1-0.273) / 607)

= 0.273     0.035441349

Lower limit = 0.273-0.035441349 = 0.237558

Upper limit = 0.273+0.035441349 = 0.308441

95% CI for P : 23.76% < P < 30.84%

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?

CI includes 0.25 , so it is possible that the true percentage is 25%.