Question

f: chi - square ($\chi^{2}$) analysis for $f_{2}$ progeny - dihybrid corn cross
use the observed (o) numbers you counted from your corn and the expected (e) numbers you just
calculated

what is your degrees of freedom (df)?
df=
use this formula:
df = number of phenotype categories - 1

use the chi - squared table to find the p - value that matches your $\chi^{2}$ and df.
p - value=
higher bound > p > lower bound
is your result statistically significant?
circle one: yes / no

human genetic characteristics
for each of the traits below:

• determine and record your phenotype (what you observe about yourself).
• then list all possible genotypes that could result in that phenotype based on whether the trait is

dominant or recessive.

example:
if a person has free earlobes (dominant), they could be ee or ee.
if a person has attached earlobes (recessive), they must be ee.

Explanation:

Step1: Calculate \((O - E)^2\)

For Purple & Smooth: \((63 - 18)^2=(45)^2 = 2025\)
For Purple & Wrinkled: \((40 - 6)^2=(34)^2=1156\)
For Yellow & Smooth: \((41 - 6)^2=(35)^2 = 1225\)
For Yellow & Wrinkled: \((44 - 2)^2=(42)^2=1764\)

Step2: Calculate \((O - E)^2\div E\)

For Purple & Smooth: \(\frac{2025}{18}=112.5\)
For Purple & Wrinkled: \(\frac{1156}{6}\approx192.67\)
For Yellow & Smooth: \(\frac{1225}{6}\approx204.17\)
For Yellow & Wrinkled: \(\frac{1764}{2}=882\)

Step3: Calculate \(\chi^{2}\)

\(\chi^{2}=112.5 + 192.67+204.17 + 882\)
\(\chi^{2}=1391.34\)

Answer:

\(\chi^{2}=1391.34\), \(df = 3\) (since number of phenotype categories \(n = 4\), \(df=n - 1=4 - 1 = 3\)). Looking at the chi - squared table, for \(df = 3\), \(\chi^{2}=1391.34\) is way beyond the values in the table (the critical values for common significance levels like \(p = 0.05\) with \(df=3\) is \(7.815\)). So \(p - value<0.001\) (since the chi - squared distribution values increase as \(p\) decreases). And the result is statistically significant (Circle Yes).