Question

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

445

green peas and

154

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.

Answer 1

Solution :

Given that,

n = 445 + 154 = 599

x = 154

Point estimate = sample proportion = = x / n = 154 / 599 = 0.257

1 - = 1 - 0.257 = 0.743

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

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

= 1.96 (((0.257 * 0.743) / 599)

= 0.018

A 95% confidence interval for population proportion p is ,

± E

= ( 0.239, 0.275 )

no,the confidence interval include 0.25, so the true percentage could easily equal 25%