A random sample of 50 musicians was taken from a population of 400 to determine

Question

A random sample of 50 musicians was taken from a population of 400 to determine how many use ear protection. Twenty of the sampled musicians used ear protection.

(a) Estimate the total number of musicians who use ear protection.

(b) Find an approximate standard error for this estimate.

(c) Of the 20 musicians who used ear protection, 12 are guitarists. Estimate the proportion of musicians who use ear protection who are guitarists. Give a standard error for this estimate.

(d) Estmate the total number of musicians who use ear protection who are guitarists. Give a standard error for this estimate.

Explanation / Answer

a)total number of musicians who use ear protection=(20/50)*400 =160

b) standard error for this estimate =(np(1-p))1/2 =(400*0.4*0.6)1/2 =9.8

c) estimated proportion =12/50 =0.24

std error of estimate =(p(1-p)/n)1/2 =0.021

d) estimation of number =np=400*0.24=96

and std deviation (np(1-p))1/2 = 8.54

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