Question

In a random sample of 115 trombone players, 13 were female. Construct a 99% confidence interval for the proportion of trombone players that are female.

Answer 1

Solution :

Given that,

n = 115

x = 13

Point estimate = sample proportion = = x / n = 13/115=0.113

1 - = 0.887

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 (((0.113*0.887) /115 )

= 0.076

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.113 +-0.076

(0.037,0.189)