Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 404 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

Solution :

Given that,

n = 404 + 161 = 565

x = 161

Point estimate = sample proportion = = x / n = 161 / 565 = 0.285

1 - = 1 - 0.285 = 0.715

a) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.285 * 0.715) / 565)

= 0.037

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.285 - 0.037 < p < 0.285 + 0.037

0.248 < p < 0.322

( 24.8% < p < 32.2% )

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