Question

A famous scientist, Mendel, conducted a genetic experiment with peas. One sample

from this experiment consisted of 152 yellow peas out of 580 peas. Calculate a 95%

confidence interval for the percentage of yellow peas. Also, find the estimation and

the margin of error.

Answer 1

Solution :

Given that,

n = 580

x = 152

Point estimate = sample proportion = = x / n = 152/580=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 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.262*0.738) / 580)

E = 0.036

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.262-0.036 < p < 0.262+0.036

0.226< p < 0.298