Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 424 green peas and 163 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?

Answer 1

Solution :

Given that,

n = 424 + 163 = 587

x = 163

a) Point estimate = sample proportion = = x / n = 163 / 587 = 0.278

1 - = 1 - 0.278 = 0.722

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.278 * 0.722) / 587)

= 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.278 - 0.036 < p < 0.278 + 0.036

( 0.242 < p < 0.314 )

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