Question

44. Suppose that you are asked to evaluate the abilities of an individual who claims to have perfect ESP (extrasensory perception). You decide to conduct an experiment to test this ability. You deal one card face down from a regular deck of 52 cards. The subject is then asked to say what the card is. Consider the following hypotheses:

    H0: The subject does not have ESP.

    H1: The subject does have ESP.

    1. (a) What would a Type I error be in this context? (Give your answer in a nonstatistical

       manner.)

    2. (b) What would a Type II error be in this context? (Give your answer in a nonstatistical manner.)

    3. (c) Suppose that you decide to conclude that the individual has ESP if and only if he or she correctly identifies the card. What is the level of significance of this particular decision rule?

    4. (d) What is the chance of a Type II error for the decision rule given in part (c)?

    5. (e) When the experiment is carried out, the individual fails to identify correctly the hidden

       card. What is the p-value?

    6. (f) When the experiment is carried out, the individual correctly identifies the hidden card.

       The p-value is 1 . Is this the chance that the null hypothesis is correct? Explain.

Subject is intro to statistics

Answer 1

(a) Type I error is the error of rejecting a true null hypothesis . That means on the basis of the test with a card from standard deck , we come to the conclusion that the subject has ESP , when actually he does not have an ESP.

(b) Type II error is the error of accepting a false null hypothesis . That means on the basis of the test with a card from standard deck , we come to the conclusion that the subject does not have  ESP , when actually he  have an ESP.

(c) Level of significance is the probability of type I error. That is probability of concluding that the person has ESP given that in reality he does not have an ESP. When we conclude that the person has an ESP ? When he identifies the card correctly . If he does not have an ESP , he guesses the card . Probability of guessing the card correctly is 1/52 = 0.0192

Thus level of significance is 0.0192

(d) Chance of type II error is the probability of concluding that he does not have an ESP , when in reality he has an ESP. When we conclude that the person does not have  an ESP ? When he cannot  identify the card correctly . Probability of not identifying the card correctly given that he has an ESP = 0.5 ( as nothing is mentioned about probability of identifying the card by an ESP person , we assume it is 0.5)

Thus chance of type II error is 0.5

(e) P value is the probability of getting the observed result when the null hypothesis is true (does not have an ESP)

Here observed result is : fail to identify  the card

Probability of  failing to identify the card when guessing is 51/52

Thus P value = 0.9808

(f) P value = P( getting the observed result when the null hypothesis is true)

= P( correctly identify the card I does not have an ESP)

Given P value = 1

That is

P( correctly identify the card I does not have an ESP) = 1

P( does not have an ESP and correctly identify the card) / P( does not have an ESP) = 1

1/52 = P( does not have an ESP)

P( null hypothesis is correct ) =1/52 = 0.0192