Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 439 green peas and 168 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.

Answer 1

Solution :

Given that,

a) n = 439 + 168 = 607

Point estimate = sample proportion = = x / n = 168 / 607 = 0.277

1 - = 1 - 0.277 = 0.723

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.277 * 0.723) / 607)

= 0.030

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.277 - 0.030 < p < 0.277 + 0.030

( 0.247 < p < 0.307 )

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