Question

-A genetic experiment with peas resulted in one sample of offspring that consisted of 434 green peas and 162 yellow peas.

a. Construct a 90​% 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?

c. Construct a 90​% confidence interval. Express the percentages in decimal form.
____<p<_____ ​(Round to three decimal places as​ needed.)

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

-​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25%
​-Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%

Answer 1

Solution :

Given that,

n = 434 +162 = 596

x = 162

a) Point estimate = sample proportion = = x / n = 162 / 596 = 0.272

1 - = 1 - 0.272 = 0.728

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 (((0.272 * 0.728) / 596)

= 0.018

A 90% confidence interval for population proportion p is ,

± E

0.272 ± 0.018

(0.254 , 0.290)

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