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Solved: Flipping and Spinning Pennies Use the data in the
Chapter 11, Problem 5 RE(choose chapter or problem)
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 |
Questions & Answers
QUESTION:
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:
Answer:
Step 1 of 2
|
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 chi-square test for independence.
Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square 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.