5 A psychic claims that she can correctly identify the astrological sign of an i

Question

5 A psychic claims that she can correctly identify the astrological sign of an individual at least 90% of the time. You test her claim by having her give the astrological sign of 7 people. You will not reject her claim if she correctly identifies the astrological sign of at least 4 of the seven people. (a) Find a. (b) Find the P-value if she correctly identifies the astrological sign of 2 of the seven people. (c) Find if she is just guessing. (Assume the 12 different astrological signs are equally probable.)

Explanation / Answer

(a) Here = Type I error

so here to calculate we have to calculate the probability of atmost 3 people out of 7 people. That would be a binomial distribution where n = 7 and p = 0.90

Pr(x <4) = BIN (x < 4 ; 7 ; 0.9) = 0.0027

(b) Here he finds astrological sign of 2 of seven people

P - value = Pr(x 2) = BIN (x 2 ; 7 ; 0.9) = 0.0002

(c) Here is type II error that means we will accept the null hypotheis even if it false.

She is purely guessing so true proportion that she is guessing only p = 1/12 = 0.0833

Here = Type II error = BINOMIAL (x 4 ; 7 ; 1/12) = 1 - BINOMIAL (x < 4 ; 7 ; 1/12) = 1 - 0.9986 = 0.0014

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.