On fan sites, there were discussions about whether the data show a home-field advantage: does the host team tend to perform better than the visiting teams? In order to answer this question, you dedicate some time to watching all 8 of the Marbula one races. For each race, you record TRUE if the host team finishes in the top 2, and FALSE otherwise. Remember, there are 16 teams competing in each race. In 2 of the 8 races, the host team finished in the top 2. You conduct a simulation of this experiment: 1000 sets of 8 races using the null proportion = a. (You need to determine the correct value of a). Of the 1000 simulated experiments shown below, you find that in b simulations, there are at least 2 races where the host team fınished in the top 2. (You determine the value of b) Simulation results Sim mean: 0.98 n- 402 400- Sim sd: 0.93 n= 350 300- 200- n=177 100- n= 59 n 12 0- # Races where host team finished in the top 2 Which of the following statements are correct? # Simulations

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Which of the following statements are correct?
The sample is the set of 8 races in the Marbula one series
The simulation p-value is 0.248 = b/1000 where b= 248 is the number of trials with a result as or
%3D
more extreme than what we observed
O The statistic is the number of races where the host finishes 1st
The research question is 'Does the host team tend to perform better than the visiting teams?
The observational unit is one marble's lap time
O We cannot conclude from this study that there is a home-track advantage that allows the home team to
perform better than would be expected by random chance alone. The results we observed could plausibly
occur by random chance.
Theory based inference is not appropriate for this problem because the sample size is not large enough (there
are not 10 successes and 10 failures)
The parameter p is the observed proportion of 16 races where the host finishes in the top 2
O Under random chance, a =
1/16 4 0.2500
O The standardized statistic is z= 1.092. z is the number of means above the standard deviation of the
distribution under the null hypothesis
O The sample size is 8 races x 16 participants 128
Transcribed Image Text:Which of the following statements are correct? The sample is the set of 8 races in the Marbula one series The simulation p-value is 0.248 = b/1000 where b= 248 is the number of trials with a result as or %3D more extreme than what we observed O The statistic is the number of races where the host finishes 1st The research question is 'Does the host team tend to perform better than the visiting teams? The observational unit is one marble's lap time O We cannot conclude from this study that there is a home-track advantage that allows the home team to perform better than would be expected by random chance alone. The results we observed could plausibly occur by random chance. Theory based inference is not appropriate for this problem because the sample size is not large enough (there are not 10 successes and 10 failures) The parameter p is the observed proportion of 16 races where the host finishes in the top 2 O Under random chance, a = 1/16 4 0.2500 O The standardized statistic is z= 1.092. z is the number of means above the standard deviation of the distribution under the null hypothesis O The sample size is 8 races x 16 participants 128
On fan sites, there were discussions about whether the data show a home-field advantage: does the
host team tend to perform better than the visiting teams?
In order to answer this question, you dedicate some time to watching all 8 of the Marbula one races.
For each race, you record TRUE if the host team finishes in the top 2, and FALSE otherwise.
Remember, there are 16 teams competing in each race.
In 2 of the 8 races, the host team finished in the top 2.
You conduct a simulation of this experiment: 1000 sets of 8 races using the null proportion = a.
(You need to determine the correct value of a). Of the 1000 simulated experiments shown below,
you find that in b simulations, there are at least 2 races where the host team finished in the top 2.
(You determine the value of b)
Simulation results
Sim mean: 0.98
n= 402
400-
Sim sd: 0.93
n = 350
300 -
200-
n= 177
100-
n= 59
n- 12
# Races where host team finished in the top 2
Which of the following statements are correct?
# Simulations
Transcribed Image Text:On fan sites, there were discussions about whether the data show a home-field advantage: does the host team tend to perform better than the visiting teams? In order to answer this question, you dedicate some time to watching all 8 of the Marbula one races. For each race, you record TRUE if the host team finishes in the top 2, and FALSE otherwise. Remember, there are 16 teams competing in each race. In 2 of the 8 races, the host team finished in the top 2. You conduct a simulation of this experiment: 1000 sets of 8 races using the null proportion = a. (You need to determine the correct value of a). Of the 1000 simulated experiments shown below, you find that in b simulations, there are at least 2 races where the host team finished in the top 2. (You determine the value of b) Simulation results Sim mean: 0.98 n= 402 400- Sim sd: 0.93 n = 350 300 - 200- n= 177 100- n= 59 n- 12 # Races where host team finished in the top 2 Which of the following statements are correct? # Simulations
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