Question

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

440

green peas and

163

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?

Answer 1

Solution :

Given that,

n = 440 + 163 = 603

x = 163

a) Point estimate = sample proportion = = x / n = 163 / 603 = 0.270

1 - = 1 - 0.270 = 0.730

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.270 *0.730) / 603)

= 0.035

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.270 - 0.035 < p < 0.270 + 0.035

( 0.235 < p < 0.305 )

( 23.5% < p < 30.5% )

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