Question

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

445

green peas and

158

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

(R

Answer 1

Solution :

Given that,

n = 445 + 158 = 603

x = 158

Point estimate = sample proportion = = x / n = 158 / 603 = 0.262

1 - = 1 - 0.262 = 0.738

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.262 * 0.738) / 603)

= 0.035

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.262 - 0.035 < p < 0.262 + 0.035

0.227 < p < 0.297

The 95% confidence interval for the population proportion p is : (0.227 , 0.297)

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