Question

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

443443

green peas and

153153

yellow peas.

a. Construct a

9090​%

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 = 443 + 153 = 596

x = 153

a) Point estimate = sample proportion = = x / n = 153 / 596 = 0.257

1 - = 1 - 0.257 = 0.743

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.257 * 0.743) / 596 )

= 0.029

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.257 - 0.029 < p < 0.257 + 0.029

( 0.228 < p < 0.286 )

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