Question

João claims he can read minds. His friend Pedro asked him to guess a number he was thinking of between 1 and 7 (inclusive). João guessed Pedro's number correctly 4 out of 9 times.
Let's test the hypothesis that João cannot read minds and therefore has a chance of
1/7 of guessing the correct number each time versus the alternative that his chance is somehow greater.
The table below sums up the results of 1000 simulations, each simulating 9 guesses with a chance of 1/7 start fraction, 1, divided by, 7, end fraction of being correct.
According to the simulations, what is the probability of having 4 or more correct guesses out of ?




Let's agree that if the observed outcome has a probability less than 1\%1%1, percent under the tested hypothesis, we will reject the hypothesis.
What should we conclude regarding the hypothesis?
Choose 1 answer:
Choose 1 answer:

(Choice A)

We cannot reject the hypothesis.

(Choice B)

We should reject the hypothesis.

correct guesses out of 9 Frequency
0 250
1 375
2 250
3 97
4 24
5 4
6 0
7 0
8 0
9 0

Answer 1

It can be deduced that the probability of having 4 or more correct guesses will be 0.0296.

How to calculate the probability

From the given information, the null hypothesis is p = 1/7 and the alternate hypothesis is p>1/7. In this case, the mind reader gets a 4 out of 9 chances.

In order to test the hypothesis, simulations for 10000 cases were run with a probability of the correct answer being 1/7.

In this case, the p-value is the probability of correct answers that are greater than 4, assuming the null hypothesis is true. Here the p-value is 0.0296.

Also, the significance level to reject the hypothesis is less than 0.01. Since p > 0.01, we then fail to reject the hypothesis. Therefore the null hypothesis stands and Joao is not a mind reader.

Learn more about probability on:

brainly.com/question/24756209