Question:
Perfect pitch is the ability to identify musical notes correctly without hearing another note as a reference. The probability that a randomly chosen person has perfect pitch is 0.0005.
Required:
a. If 20 students at Julliard School of Music art tested, and 2 are found to have perfect pitch, would you conclude at the .01 level of significance that Julliard students are more likely than the general population to have perfect pitch?
b. Show that normality of the sample proportion p should not be assumed.
Answer:
See explanation below
Explanation:
Given:
Sample size, n = 20
Probability that a chosen person has perfect pitch = 0.0005
x
Level of significance = 0.01
a) Let's find the probability of 2 or more people with perfect pitch using bimonial distribution.
P(2 or more with perfect pitch ) =
P(x≥2) = 1 - P(x≤1)
P(x≥2 | n=20, p'=0.0005) = 0.00005
Since the probability of getting 2 or more people with perfect pitch, 0.00005, is significantly lower than the level of significance, 0.01, we conclude that Julliard students are more likely than the general population to have perfect pitch.
b) For normality to be assumed, [tex] n * \pi _0 [/tex] should be ≥5 for normal approximation.
Since [tex] n * \pi _0 [/tex] is too small, normality cannot be assumed.
