In: Statistics and Probability
Weekly Experiment and Discussion
B) Using the compiled results ( to be posted on Day #4), can you conclude the results of each coin were independent? ( Show your supporting work)
Note: For each, it is about interpreting the results versus any
preconceived notions you may have about this exercise
Here is a table that summarizes the coin toss results.
HH 183
HT 185
TH 161
TT 172
We have to perform chi square test for independence.
H0 : Results of each coin are independent.
Ha : Results of each coin are not independent .
Expected frequency = Total frequency / 4 = ( 183+185+161+172 ) / 4 = 172.25
Now we have to find chi square test statistic
2 = ; O is observed frequency and E is expected frequency.
Therefore 2 = 2.1041
Critical value :
We are not given level of significance α , so assume 0.05
Degrees of freedom (df) = (r-1) r is types of an outcome ( HH , HT, TH , TT )
r = 4
df =4 - 1 = 3
Therefore critical value χ2(0.05,3) = 7.815 -------- ( From chi square table )
Critical region : Reject H0 if χ2 is greater than χ2(0.05,3) = 7.815
fail to reject H0 , if χ2 is less than χ2(0.05,3) = 7.815
Decision :
As 2.1041 is less than 7.815 we fail to reject H0
We fail to reject H0, so accept H0
Conclusion: Results of each coins are independent.