Question

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

426 green peas and 168 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?

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

nothingless than<p less than<nothing

​(Round to three decimal places as​ needed.)

b. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?

​Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%

​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%

Answer 1

Solution :

Given that,

n = 426 + 168 = 594

x = 168

a) Point estimate = sample proportion = = x / n = 168 / 594 = 0.283

1 - = 1 - 0.283 = 0.717

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 (((0.283 * 0.717) / 594 )

= 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.283 - 0.036 < p < 0.283 + 0.036

( 0.247 < p < 0.319)

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