Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 435 green peas and 152 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 = 435 + 152 = 587

x = 152

Point estimate = sample proportion = = x / n = 152 / 587 = 0.259

1 - = 1 - 0.259 = 0.741

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.259 * 0.741) / 587)

= 0.035

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.259 - 0.035 < p < 0.259 + 0.035

( 0.224 < p < 0.294 )

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