Question 1209020: genetic experiment with peas resulted in one sample of offspring that consisted of 447 green peas and 158 yellow peas.
a. Construct a 95% confidence interval to estimate of the percentage of yellow peas
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = number of yellow peas = 158
n = sample size = 447 green + 158 yellow = 605 total.
phat = sample proportion of yellow peas
phat = x/n
phat = 158/605
phat = 0.26115702 approximately
Around 26.12% of the peas in the sample are yellow.
At 95% confidence, the z critical value is roughly z = 1.960
This is a value to memorize since it comes up a lot in statistics.
Or this value is something you would look up in a textbook, reference sheet, or website.
E = margin of error for a proportion
E = z*sqrt(phat*(1-phat)/n)
E = 1.960*sqrt(0.26115702*(1-0.26115702)/605)
E = 0.03500300
L = lower boundary of the confidence interval
L = phat - E
L = 0.26115702 - 0.03500300
L = 0.22615402
L = 0.226
U = upper boundary of the confidence interval
U = phat + E
U = 0.26115702 + 0.03500300
U = 0.29616002
U = 0.296
The 95% confidence interval in the format L < p < U is approximately 0.226 < p < 0.296
This can be condensed to (0.226, 0.296)
It indicates we are 95% confident that the population proportion of yellow peas is somewhere between 22.6% and 29.6%
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