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.

(a)	If 38 students at Julliard School of Music are tested, and 1 are found to have perfect pitch, would you conclude at the 0.01 level of significance that Julliard students are more likely than the general population to have perfect pitch?
	No Yes

(b)	Normality should not be assumed because

a.	only 1 students had perfect pitch.
b.	the product of n and π0π0 is too small.
c.	all students had perfect pitch.
d.	no student had perfect pitch.

	a b c d

Answer 1

Answer a) Yes

Sample proportion p̂ = 1/38 = 0.0263

Z Test statistic = (0.0263-0.0005)/sqrt(0.0005*(1-0005)/38) = 7.12

P-value for z = 7.12 for a right tailed test is 0.000.

Since p-value is less than 0.01, we can say that Julliard students are more likely than the general population to have perfect pitch

Answer b)

Normality should not be assumed because only 1 students had perfect pitch.