Question

You ask 30 students if they like your fancy new hat. 25 of these students like your hat. What is the 95% confidence interval for the proportion of students who like your hat?

The answer is (0.70, 0.97), please explain how [show working].

Answer 1

solution:

Given data

Total no.of students (n) = 30

No.of students like your hat (X) = 25

The sample proportion = X/n

= 25/30

= 0.833

For 95% Confidence interval = 1 - CL = 1 - 0.95 = 0.05

The critical value Zc = Z(/2) = Z(0.025) = 1.96 [ using Z distribution table]

The confidence interval for Proportion is given by

CI :   ± Zc *

: 0.833  ± 1.96 *

: 0.833 ± 0.133

: ( 0.700 , 0.966)

CI :(0.70 , 0.97) [ Rounded to 2 decimal places ]

Therefore, we are 95% confident that proportion of students who like your hat is between 0.70 and 0.97