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

Question

A genetic experiment with peas resulted in one sample of offspring that consisted of 441 green peas and 165 yellow peas. Construct a 95% confidence interval to estimate of the percentage of yellow peas. 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? Construct a 95% confidence interval. Express the percentages in decimal form. 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%

Explanation / Answer

Since this is a binomial distribution (only yellow or green outcomes) this is fairly straightforward:

Yellow=165

green peas=441

Total=606

yellow = 165/606 total =0.2722~ 27.22%
green = 441/606 total = 72.77%

SD = sqrt((p)(1-p)/n) = sqrt((0.2722)(.7277)/606) = 0.0180 = 1.8%

The two-tailed Z-value for 95% is 1.96.

So now your 95% confidence interval is going to be 27.22% +/- 1.8%(1.96), which is +/- 3.526. This then gives you:

27.22 - 3.526 = 23.8
27.22 + 3.526 = 30.9

So you can say your probability of having a yellow pea, p, is 0.238 < p < 0.309.

B. Answer is Yes

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