A binomial model shows that two outcomes have the same probability of occurring. In an experiment with 60 trials to test this model, the researcher found that Outcome A occurred 36 times. How did the experimental outcome compare to the theoretical model?
Outcome A had an expected probability of 50% but an actual probability of 36%.
Outcome B occurred 36% of the time rather than the expected 50%.
The result for Outcome B was 4 less than expected.
The result for Outcome A was 6 more than expected.
To compare the experimental outcome to the theoretical model in this binomial experiment, we need to calculate the expected probabilities of the outcomes and then compare them to the actual observed frequencies.
In this case, the binomial model assumes that both outcomes have an equal probability of occurring. So, in a fair situation, each outcome should have a probability of 50%.
The expected probability for Outcome A is 50%, as mentioned in the question. However, in the experiment, Outcome A occurred 36 times out of 60 trials. To find the actual probability, we divide the number of occurrences by the total number of trials:
Actual probability of Outcome A = Number of occurrences / Total number of trials
Actual probability of Outcome A = 36 / 60 = 0.6 or 60%
Comparing the expected and actual probabilities of Outcome A, we see that the actual probability is higher (60%) than the expected probability (50%). So, the result for Outcome A was 10% (6 more) above what was expected.
Now, let's consider Outcome B. Since there are only two outcomes in a binomial experiment where both have the same probability, the probability of Outcome B is also expected to be 50%. However, the question does not mention the frequency of Outcome B occurring in the experiment.
Therefore, we cannot make any specific statements about the result for Outcome B based on the given information. The only information provided is about the observed frequency of Outcome A.