Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 414 green peas and 154 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. nothingless thanpless than nothing ​(Round to three decimal places as​ needed.) b. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations? ​No, the confidence interval includes​ 0.25, so the true percentage could easily equal​ 25% ​Yes, the confidence interval does not include​ 0.25, so the true percentage could not equal​ 25%

Answer 1

Answer: a. The interval in percentage is (23.46% , 30.76%)

b. No

Step-by-step explanation: To determine the confidence interval of a proportion, first find the percentage of yellow in that population:

phat = $\frac{154}{414+154}$

phat = 0.2711

The level α is 95%

1 - α = 0.05

α/2 = 0.025

As the population is bigger than 30, use z-test.

According to the table, z-score for α/2 = 0.025 is z = 1.96

The error for the interval is:

E = z.$\sqrt{\frac{phat(1-phat)}{n} }$

E = 1.96.$\sqrt{\frac{0.2711(1-0.2711)}{568} }$

E = 1.96*0.01865

E = 0.0365

The lower and higher limits of the interval are:

phat - E = 0.2711 - 0.0365 = 23.46%

phat + E = 0.2711 + 0.0365 = 30.76%

In conclusion, the 95% confidence interval to estimate the percentage of yellow is (23.46%,30.76%)

b. No, because 25% is inside the interval meaning that it doesn't contradict the expectations.