Question

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

436

green peas and

151

yellow peas.

A. Construct a

90%

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

90​%

confidence interval. Express the percentages in decimal form.

nothingless than<pless than<nothing

​(Round to three decimal places as​ needed.)

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

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

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

Answer 1

Sample proportion of yellow peas = 151 / (151 + 436) = 151 / 587 = 0.257

a)

90% confidence interval for p is

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

0.257 - 1.645* sqrt( 0.257 * 0.743 / 587) < p < 0.257 + 1.645* sqrt( 0.257 * 0.743 / 587)

0.227 < p < 0.287

b)

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