Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 416 green peas and 154 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​ expectationsa.

A.) Construct a 90​% confidence interval.

Express the percentages in decimal form: __< p < ___ (Round to three decimal places as​ needed.)

B.)Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations? ​

Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25% ​

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

Answer 1

Solution :

n = 416 green peas +  154 yellow peas = 570 oeas

x = 154 yellow peas

= x / n = 154 / 570 = 0.270

1 - = 1 - 0.270 = 0.730

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

= 1.645 * (((0.270 * 0.730) / 570)

= 0.030

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.270 - 0.030 < p < 0.270 + 0.030

0.240 < p < 0.300

b) Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%