Question

Construct a 95% confidence interval by hand for what proportion of students are vegan, if you took a random sample of 100 students and 3 were vegan.

Answer 1

Solution :

n = 100

x = 3

= x / n = 3 / 100 = 0.030

1 - = 1 - 0.030 = 0.970

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 * (((0.030 * 0.970) / 100)

= 0.033

A 95 % confidence interval for population proportion p is ,

- E < P < + E

0.030 - 0.033 < p < 0.030 + 0.033

- 0.003 < p < 0.063

The 95% confidence interval for the population proportion p is : (- 0.003 , 0.066)