Question

In an experiment in extrasensory perception (ESP), a subject in one room is asked to state the color (red or blue) of a card chosen from a deck of 50 well-shuffled cards by an individual in another room. It is unknown to the subject how many red or blue cards are in the deck.

a.)

What are your null and alternate hypotheses in this case?

b.)

If the subject identifies 32 cards correctly, determine the chances of each hypothesis being correct. Use the Gaussian approximation to the binomial distribution in making your calculations. Are these results are significant at either the 5% and 1% levels?

Answer 1

(a)

We are checking if the person has ESP or not.

Since the person has no idea of the colour of the card chosen and also there are two colours to choose from, the person will have an equal probability of choosing correctly and incorrectly, if he does not have ESP(correct colour by mere guessing). But if he has he will have more chances of choosing the correct colour(more than just a mere guess).

:Does not have ESP   

:Has ESP

(b)

We have

Using Gaussian Approximation where X=32

Test Stats

...............................sub values

Decision Criteria

Reject if

(1)

at

Looking at the values we reject since 2.06239>1.6449 at

Conclude that people have ESP at 95% confidence interval and chances of getting correct colour 32 out of 50 times is less than 5% when only merely guessing.

(2)

at

Looking at the values we do not reject since 2.06239<2.3263 at

Conclude that individual doesn't have ESP at 90% Confidence Interval and chances of getting correct colour 32 out of 50 times is not less than 1% when only merely guessing.

Please let me know if you have any doubts by mentioning them in the comments section.