Question

Weekly Experiment and Discussion

• Take 2 coins and flip "together" 50 times
• Tally each set of flips and report the frequencies in the format shown below:

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

Answer 1

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.