Chapter PVII, Problem 1RE

To determine

To conduct: a suitable hypothesis and give the conclusion on the basis of given information.

Explanation of Solution

Given:

Trait	Observed counts
Attached-non-curling	10
Attached-curling	22
Free-non-curling	31
Free curling	59

Formula used:

  ${\chi }^2={\displaystyle \sum \frac{{\left(Obs-Exp\right)}^2}{Exp}}$

Calculation:

State the null and alternative hypothesis

  $H_0:$ outcomes observed is consistent along with the genetic theory.

  $H_1:$ outcomes observed is not consistent along with the genetic theory.

Traits is 1:3:3:9 this means that from 122 units, the expected number of these with

attached and non-curling trait is

  $\begin{array}{l}122\times \frac{1}{\left(1+3+3+9\right)}\\ =122\times \frac{1}{16}\\ =7.625\end{array}$

Attached curling is

  $\begin{array}{l}122\times \frac{3}{\left(1+3+3+9\right)}\\ =122\times \frac{3}{16}\\ =22.875\end{array}$

In this similar way estimated all expected values

Trait	Expected counts
Attached-non-curling	7.625
Attached-curling	22.875
Free-non-curling	22.875
Free curling	68.625

  

From the above output P-value is 0.1711 which is high and therefore not reject the null hypothesis which means that the observed traits are in the accordance with the genetic theory.