Mar 7

${\chi }^2$ Test

We are considering using a Chi-square goodness-of-fit test to check if the distribution of Tobacco plants is the same as the claimed distribution.

• $H_0$: The distribution of Tobacco plants is the same as the claimed distribution
• $H_a$: The distribution of Tobacco plants is not the same as the claimed distribution
  $H_0$ : $P_1=\frac{1}{4}/P_2=\frac{1}{2}{P}_3=\frac{1}{4}$
  $H_a$ : At least 2 of the $P_i$ is incorrect
• Random: The data come from a random sample or a randomized experiment
• Large Sample Size: All expected counts are at least 5
• Independent: Individual observations are independent. When sampling without replacement, check that the population is at least 10 times as large as the sample (the 10% condition).

$${\chi }^2=\sum _{i=1}^n\frac{({\text{Observed}}_i-{\text{Expected}}_i{)}^2}{{\text{Expected}}_i}\approx 6.4761904761905$$

• $df=\text{Number of categories}-1=2$
• ${\text{Expected}}_i=n_i\times p_i$
• $p_{val}=0.039\le \alpha$ : Reject $H_0$

If reject, which category contribute the most to the rejection? $P_3$
We have sufficient statistical evidence that the distribution of Tobacco plants differ significantly from the claimed distribution.