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 .0005.

(a). If 20 students at Julliard School of Music are tested, and 3 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). Find the p-value for the testing problem in part (a).

(c) . How large a sample size is needed to estimate the population proportion within 0.001 with 99% confident?

Answer 1

(a)

Ho: p = 0.0005

Ha: p > 0.0005

test statistics

x = 3, n = 20

= x/ n = 3/20 = 0.15

z stat = 29.9075

z critical for level of significance 0.01 : ± 2.58

As z stat falls in the rejection area, we reject the Null hypothesis.  

(b) p value = p(z > 29.9075) = 1-1 = 0

(c) Margin of error = 0.001

z value for 99% CI = 2.576

n = 846016.44