A population geneticist is studying the genes found at two

Chapter 6, Problem 10E

(choose chapter or problem)

A population geneticist is studying the genes found at two different locations on the genome. He estimates the proportion \(p_{1}\) of organisms who have geneA at the first locus to be \(\hat{p}_{1}=0.42\), with uncertainty \(\sigma_{1}=0.049\). He estimates the proportion of organisms that have gene B at a second locus to be \(\hat{p}_{2}=0.23\), with uncertainty \(\sigma_{2}=0.043\). Under assumptions usually made in population genetics (Hardy–Weinberg equilibrium), \(\hat{p}_{1}\) and \(\hat{p}_{2}\) are independent and normally distributed, and the proportion p of organisms that have both genes A and B is estimated with \(\hat{p}=\hat{p}_{1} \hat{p}_{2}\).

a. Compute \(\hat{p}\) and use propagation of error to estimate its uncertainty.

b. Assuming \(\hat{p}\) to be normally distributed, find the P-value for testing \(H_{0}: p \geq 0.10\).

c. Generate an appropriate simulated sample of values \(\hat{p}^{*}\). Is it reasonable to assume that \(\hat{p}\) is normally distributed?

Equation Transcription:

Text Transcription:

p_1

p_1=0.42

sigma_1=0.049

p_2=0.23

sigma_2=0.043

hat{p}1

hat{p}2

hat{p}=hat{p}1hat{p}2

hat{p}

hat{p}

H_0:p{>/=}0.10

hat{p}^*

hat{p}