Question

An insurance company checks police records on 596 accidents selected at random and notes that teenagers were at the wheel at 87 of them. if we want to construct a 95% confidence interval for the proportion of all auto accidents that involve teenage drivers, what would be the standard error of the sample proportion of successes?

Answer 1

Solution :

Given that,

n = 596

x = 87

Point estimate = sample proportion = = x / n = 87 / 596 = 0.146

1 - = 1 - 0.146 = 0.854

standar error = =  [p ( 1 - p ) / n] =   [(0.146 * 0.854) / 596 ] = 0.0145

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

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

= 1.96 (((0.146 * 0.854) / 596 )

= 0.028

A 95% confidence interval for population proportion p is ,

± E   

= 0.146  ± 0.028

= ( 0.118, 0.174 )