Question

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

408

green peas and

162

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.

nothing<p<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?

​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 = 408 + 162 = 570

x = 162

a) Point estimate = sample proportion = = x / n = 162 / 570 = 0.284

1 - = 1 - 0.284 = 0.716

Z/2 = Z_0.025 = 1.96

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

= 1.96 (((0.284 * 0.716) / 570 )

= 0.037

A 95% confidence interval for population proportion p is ,  

- E < p < + E

0.284 - 0.037 < p < 0.284 + 0.037

( 0.247 < p < 0.321 )

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