Question

a. given the results of your own experiment, can you conclude the results of each coin were independent? (show your supporting work)

b. using the compiled results, can you conclude the results of each coin were independent? (show your supporting work)

Note: its about interpreting the results.

my own results:

2nd coin heads 2nd coin tails

1st coin heads 8 12

1st coin tails 16 14

compiled results:

2nd coin heads 2nd coin tails

1st coin heads 188 214

1st coin tails 171 177

Answer 1

a)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	E	G					Total
N	24*20/50=9.6	26*20/50=10.4					20
M	24*30/50=14.4	26*30/50=15.6					30

	(fo-fe)^2/fe
N	0.267	0.246
M	0.178	0.164

Ho: given two variable are independent
H1: Given two variables are not independent

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   0.855                  
                      
Level of Significance =   0.05                  
Number of Rows =   2                  
Number of Columns =   2                  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1                  
                      
p-Value =   0.3552   [Excel function: =CHISQ.DIST.RT(χ²,df) ]              
Decision:    p value > α , do not reject Ho                  

We can conclude the results of each coin were independent

c)

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	E	G					Total
N	359*402/750=192.424	391*402/750=209.576					402
M	359*348/750=166.576	391*348/750=181.424					348

	(fo-fe)^2/fe
N	0.102	0.093
M	0.117	0.108

Ho: given two variable are independent
H1: Given two variables are not independent

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   0.420                  
                      
Level of Significance =   0.05                  
Number of Rows =   2                  
Number of Columns =   2                  
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1                  
                      
p-Value =   0.5167   [Excel function: =CHISQ.DIST.RT(χ²,df) ]              
Decision:    p value > α , do not reject Ho                  

We can conclude the results of each coin were independent

THANKS

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