Question

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

417

green peas and

159

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.

less than<pless than<

​(Round to three decimal places a

Answer 1

Solution :

Given that,

n = 417 + 159 = 576

x = 159

a) Point estimate = sample proportion = = x / n = 159 / 576 = 0.276

1 - = 1 - 0.276 = 0.724

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 (((0.276 * 0.724) / 576)

= 0.037

A 95% confidence interval for population proportion p is ,  

- E < p < + E

0.276 - 0.037 < p < 0.276 + 0.037

( 0.239 < p < 0.313 )

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