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Electrical Stimulation for Fresh Insight? We use the data in Table 1 to conduct a randomization test to see if there was evid

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The null and alternative hypotheses are   
Ho : There is no relationship between Treatment and Problem Solving   
Ha :   There is no relationship between Treatment and Problem Solving   
   
Let Level of Significance α = 0.05   
We use Chi Square test of independence   
   
Grand Total of frequencies = 40   
To find Expected Frequencies   
Expected Frequencies = (Row Total * Column Total)/Grand Total   

Expected Frequencies (E) Solved Not Solved
Sham 8 12
Electrical 8 12

Following table gives the value of (Observed - Expected)² / Expected

Solved Not Solved
Sham 2 1.3333
Electrical 2 1.3333

Chi Square Value = ∑[(Observed - Expected)² / Expected]   
χ² = 6.6667   
   
Degrees of freedom = df = (number of rows - 1) * (number of columns - 1)   
Degrees of freedom = df = 1   
   
From chi square table or CHISQ.DIST.RT(X, df) function of Excel   
we find the p-value   
p-value = CHISQ.DIST.RT( 6.6667, 1) = 0.0098   
p-value = 0.0098   
   
Decision :   
0.0098 < 0.05   
that is p-value <= α   
Hence we REJECT Ho   
   
Conclusion :   
There exists enough statistical evidence at α = 0.05 to show that    
there is a relationship between problem solving and treatment   
Thus electrical simulation helped people solve a problem that requires fresh insight   

Normal Distribution and Chi Square Distribution
The variables in the problem are nominal variables. The chi-square test is used mainly when dealing with a nominal variable

Also it is required to test interaction between two variables, which cannot be tested using normal distribution.

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