During the 2010 World Cup tournament, Paul the Octopus (in a German aquarium) became famous for correctly predicting the winner in all 8 games it was asked to predict. (Two containers of food were lowered into Paul's tank, each with a flag of the opposing teams. He made a selection by choosing which container to eat from. Check out the video on YouTube!) Is this evidence that Paul has psychic powers and can choose correctly more than half the time? State the null and alternative hypotheses: What is Paul's sample proportion? We want to see how unlikely it is to have an 8 for 8 record if Paul is just randomly guessing. We can simulate this with a coin! Each coin flip represents a guess between two teams, with "heads" standing for a correct guess and "tails" for incorrect. Why does this method work for assuming the null hypothesis is true? Flipping a coin 8 times and recording the proportion of heads counts as one simulation. A ran- domization distribution of 1000 such simulations is shown on the next page. Out of these 1000 simulations, the simulated sample proportion was 1 on 4 of them. What is the p-value for the sample statistic of 1?
During the 2010 World Cup tournament, Paul the Octopus (in a German aquarium) became famous for correctly predicting the winner in all 8 games it was asked to predict. (Two containers of food were lowered into Paul's tank, each with a flag of the opposing teams. He made a selection by choosing which container to eat from. Check out the video on YouTube!) Is this evidence that Paul has psychic powers and can choose correctly more than half the time? State the null and alternative hypotheses: What is Paul's sample proportion? We want to see how unlikely it is to have an 8 for 8 record if Paul is just randomly guessing. We can simulate this with a coin! Each coin flip represents a guess between two teams, with "heads" standing for a correct guess and "tails" for incorrect. Why does this method work for assuming the null hypothesis is true? Flipping a coin 8 times and recording the proportion of heads counts as one simulation. A ran- domization distribution of 1000 such simulations is shown on the next page. Out of these 1000 simulations, the simulated sample proportion was 1 on 4 of them. What is the p-value for the sample statistic of 1?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:During the 2010 World Cup tournament, Paul the Octopus (in a German aquarium) became famous
for correctly predicting the winner in all 8 games it was asked to predict. (Two containers of food
were lowered into Paul's tank, each with a flag of the opposing teams. He made a selection by
choosing which container to eat from. Check out the video on YouTube!) Is this evidence that Paul
has psychic powers and can choose correctly more than half the time?
State the null and alternative hypotheses:
What is Paul's sample proportion?
We want to see how unlikely it is to have an 8 for 8 record if Paul is just randomly guessing. We
can simulate this with a coin! Each coin flip represents a guess between two teams, with "heads"
standing for a correct guess and "tails" for incorrect. Why does this method work for assuming the
null hypothesis is true?
Flipping a coin 8 times and recording the proportion of heads counts as one simulation. A ran-
domization distribution of 1000 such simulations is shown on the next page. Out of these 1000
simulations, the simulated sample proportion was 1 on 4 of them. What is the p-value for the
sample statistic of 1?
Transcribed Image Text:2
Randomization Dotplot of Proportion Null hypothesis: p = o.s
Left Tail Two-Tail✓ Right Tail
300
250
200
150
100
50
0.0
0.1
0.2
0.3
0.4
ds
null - 0.5
0.6
0.7
#samples 1000
mean-0.505
st.dev.= 0.175
0.8 0.9
Orig
Co
Ran
Co
0.004
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