SOLUTION: Hello, I am working on the following statistics problem: Using the following cannabis abuse treatment distribution, please compute the decision rule value and the Chi-Square v

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Question 928151: Hello,
I am working on the following statistics problem:
Using the following cannabis abuse treatment distribution, please compute the decision rule value and the Chi-Square value. Then draw your conclusion.
Heavy Use, Recreational Use, No Use
Treatment 15, 15, 45
No Treatment 50, 15, 10
Below is what I've started with, but not sure if I'm on the right track?
1. Set up hypotheses: Ho: There is no difference between cannabis use in the treatment and no treatment groups. (Ho µ=µo)
H1: There is a difference between the cannabis use in the treatment vs. no treatment groups. (H1 µ ≠ µo)
*Alpha= 0.05
2. Select Appropriate test: Both variables are categorical; use Chi-Square test of independence
3. Degrees of freedom= rows-1 x columns-1= 1 * 2= 2; critical x²= 5.99; reject Ho if x² ≥ 5.99; fail to reject Ho if x²<5.99
4. Test statistic: O= observed, E= expected; (O-E); (O-E) ²/E:
Your help is greatly appreciated.
Thank you,
Jillian
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
I am working on the following statistics problem:
Using the following cannabis abuse treatment distribution, please compute the decision rule value and the Chi-Square value. Then draw your conclusion.
Heavy Use, Recreational Use, No Use
Treatment 15, 15, 45
No Treatment 50, 15, 10
Ho: Row and Column factors are independent
H1: Row and Column factos are dependent
*Alpha= 0.05
2. Select Appropriate test: Both variables are categorical; use Chi-Square test of independence
-----
I ran a Chi-Sq Test on the DATA and got the following::
test stat:: Chi-Sq = 1.12
p-value = 1.18*10^-9
degrees of freedom:: (2-1)(3-1) = 2
-------
Conclusion: Since the p-value is less than 5%, reject Ho.
The row and column factors are dependent.
------------
Cheers,
Stan H.
------


Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi

	       Heavy Use,	Recreational Use,     No Use      tot

Treatment	   15	          15	               45          75

exp                       32.5            15                   27.5

No Treatment	   50	          15	               10          75

Exp                       32.5            15                   27.5

tot                              65                   30                   55           150

 = 75*65/150 = 32.5

 = 75*30/150 = 15

 = 75*55/150 = 27.5

 = 75*65/150 = 32.5

 = 75*30/150 = 15

 = 75*55/150  = 27.5

..........

X^2 = (15-32.5)^2/32.5 + (15-15)^2/15 + (45-27.5)^2/27.5 + (50-32.5)^2/32.5 + (15-15)^2/15 + (10-27.5)^2/27.5 = 9.42 + 11.14 +  9.42 + 11.14 = 41.11 

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