Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 447 green peas and 156

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?

a. Construct a 90​%

confidence interval. Express the percentages in decimal form.

nothingless than<pless than<nothing

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

Answer 1

Solution :

Given that,

a) Point estimate = sample proportion = = x / n = 156 / 603 = 0.259

1 - = 1 - 0.259 = 0.741

Z/2 = Z0.05 = 1.645

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

= 1.645(((0.259 * 0.741) / 603)

= 0.029

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.259 - 0.029 < p < 0.259 + 0.029

( 0.230 < p < 0.288 )

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