Question

A genetic experiment with peas resulted in one sample of offspring that consisted of

418418

green peas and

154154

yellow peas.a. Construct a

9595​%

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.

Answer 1

a)

Sample proportion = 154 / (154 + 418) = 154 / 572 = 0.269

95% confidence interval for p is

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

0.269 - 1.96 * sqrt( 0.269 * 0.731 / 572 ) < p < 0.269 + 1.96 * sqrt( 0.269 * 0.731 / 572 )

0.233 < p < 0.305

95% CI is ( 0.233 , 0.305 )

b)

Since claimed proportion 0.25 lies in confidence interval calculated in part a) , we do not have

sufficient evidence to reject the null hypothesis.

The result does not contradict the expectation.