When Gregor Mendel (born 1822, died 1884) conducted his famous genetics experiment with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas. in Mendel's theory such experiments yield a characteristic distribution of colors, but each individual plant is an independent trial that may have one color or the other.
a) calculate a 95% confidence interval for the population proportion of yellow offspring. (5 points)
b) according to Mendel's theory the proportion of yellow offspring in this experiment should be 25%. Based on the confidence interval calculated in part a) assess whether the results of this experiment are consistent with Mendel's theory. Justify your answer. (3 points)
c) suppose someone says "well, the experimental proportion was over 26% and you can't go against the evidence. it looks like Mendel should have adjusted his theory" provide an appropriate answer. (3 points)