Test the goodness of fit of the data to the genetic model given in Problem 55 of Chapter...

Test the goodness of fit of the data to the genetic model given in Problem 55 of Chapter 8.

Reference

For two factors—starchy or sugary, and green base leaf or white base leaf—the following counts for the progeny of self-fertilized heterozygotes were observed (Fisher 1958):

According to genetic theory, the cell probabilities are .25(2 + θ), .25(1 − θ), .25(1 − θ), and .25θ, where θ(0 < θ < 1) is a parameter related to the linkage of the factors.

a. Find the mle of θ and its asymptotic variance.

b. Form an approximate 95% confidence interval for θ based on part (a).

c. Use the bootstrap to find the approximate standard deviation of the mle and compare to the result of part (a).

d. Use the bootstrap to find an approximate 95% confidence interval and compare to part (b).