Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 427 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?

Construct a 95​%confidence interval. Express the percentages in decimal form.

Answer 1

Solution :

Given that,

a) n = 427 + 154 = 581

Point estimate = sample proportion = = x / n = 154 / 581 = 0.265

1 - = 1 - 0.265 = 0.735

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.265 * 0.735) /581 )

= 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.265 - 0.036 < p < 0.265 + 0.036

( 0.229 < p < 0.301 )

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