Question

15 out of 54 attempts were successful in an experiment. Obtain a 96% confidence interval.

We are 96% confident that the percentage of successful attempts is between (lower bound) ________ and (upper bound) _________.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 15 / 54 = 0.278

1 - = 1 - 0.278 = 0.722

Z/2 = Z_0.02 = 2.054  

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

= 2.054 (((0.278 * 0.722) / 54 )

= 0.125

A 96% confidence interval for population proportion p is ,

± E   

= 0.278  ± 0.125

= ( 0.153, 0.403 )

We are 96% confident that the percentage of successful attempts is between 0.153 and 0.403.