Problem 5RE
Flipping and Spinning Pennies Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in Chance News)Does the conclusion change if the significance level is changed to 0.01?

Heads 
Tails 
Flipping 
2048 
1992 
Spinning 
953 
1047 
Answer:
Step 1 of 2</p>

Heads 
Tails 
Total 
Flipping 
2048 
1992 
4040 
Spinning 
953 
1047 
2000 
Total 
3001 
3039 
6040 
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H0: The claim that when flipping or spinning a penny, the outcome is independent
H1: The claim that when flipping or spinning a penny, the outcome is not independent
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chisquare test for independence.
Applying the chisquare test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chisquare test statistic.
DF = (r  1) (c  1) = (2  1) (2  1) = 1

Heads 
Tails 
Total 
Flipping 
2048 
1992 
4040 
Spinning 
953 
1047 
2000 
Total 
3001 
3039 
6040 
= 2007.2913
= 2032.7086
= 993.7086
= 1006.2913
SL.No 
O 
E 
(O  E )2 
(O  E)2/E 
1 
2048 
2007.2913 
1657.198 
0.825589318 
2 
1992 
2032.7086 
1657.19 
0.815262017 
3 
953 
993.7086 
1657.19 
1.66768217 
4 
1047 
1006.2913 
1657.198 
1.646837507 
Sum 
6040 
6039.9998 
6628.777 
4.955371012 
The calculation continues as follows. Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome.