Scientists wish to test the mind-readiing ability of a person who claims to have ESP. They use five cards with different and distinctive symbols( square, cicrle, triangle, line, squiggle). Someone picks a card at random and thinks about the symbol. The mind-reader must correctly identify which symbol was on the card. If the test consists of 100 trails, how many would this person need to get right in order to convince you that ESP may actuLLY EXIST. EXPLAIN
nEED SOME HELP THANK YOU
To determine how many correct identifications would be needed to believe in the existence of ESP, we can use statistical analysis.
First, let's establish a baseline. Since there are five different symbols on the cards, if the person were randomly guessing without ESP, we would expect them to get the correct answer about 20% of the time (1 out of 5). In this case, "random" means there is no influence from ESP, just chance guessing.
Now, let's set a level of significance for the test. This level represents how confident we want to be in our conclusion. A common value for the level of significance is 5% (0.05). This means that we are willing to accept a 5% chance of making a type I error, which is concluding that ESP exists when it actually doesn't.
To evaluate whether the person's performance is beyond random chance, we can use statistical hypothesis testing. A commonly used test is the binomial test, which is appropriate when we have a fixed number of trials (100 in this case) and two possible outcomes (correct or incorrect).
Using the binomial test, we can calculate the probability of getting a certain number of correct guesses or better purely by chance. If this probability is below our chosen level of significance (0.05), we can reject the null hypothesis (the person is guessing at random) and consider the possibility of ESP.
Let's consider a scenario where the person gets 30 correct guesses out of the 100 trials. We can calculate the probability of getting this result or a more extreme result purely by chance. If this probability is less than 0.05, we can say that it's unlikely to have occurred due to random guessing alone.
To calculate this probability, we can use statistical software, online calculators, or the binomial distribution equation. For simplicity, let's use an online calculator. When plugging in the values (100 trials, 30 successes, baseline probability 0.2), we find that the probability is approximately 0.049.
Since this calculated probability is just below our chosen level of significance (0.05), we can conclude that it is possible that ESP exists. However, it's important to note that this result alone doesn't prove the existence of ESP. Further testing and replication of the results would be required for stronger evidence.
In summary, the person would need to consistently perform significantly better than what random guessing would predict, with a calculated probability below the chosen level of significance, to consider the existence of ESP as a plausible explanation.