Question

I have over 400 songs on my mobile phone. I want to estimate what proportion of the songs are by a male artist. I wrote a list of 50 songs and found that 20 of those songs were by male artists.

Based on my sample, what is the 95% confidence interval for the proportion of songs that are by a male artist?

Please show how you determined this.

Answer 1

Solution :

Given that,

n = 50

x = 20

= x / n = 50 / 20 = 0.400

1 - = 1 - 0.40 = 0.600

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

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

= 1.960 * (((0.400 * 0.600) / 50)

= 0.136

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.400 - 0.136 < p < 0.400 + 0.136

0.264 < p < 0.536

The 95% confidence interval for the population proportion p is : ( 0.264 , 0.536)