Question

A random sample of 100 suspension helmets used by motorcycle riders and automobile race-car drivers was subjected to an impact test, and on 36 of these helmets some damage was observed. Using the traditional method (not plus 4) find a 95% confidence interval for the true proportion of helmets that would sustain damage in this testing. Be sure to assess assumptions and interpret the interval in context.

Answer 1

Solution :

Given that,

n = 100

x = 36

Point estimate = sample proportion = = x / n = 36 / 100 = 0.36

1 - = 1 - 0.36 = 0.64

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 (((0.36 * 0.64) / 100 )

= 0.094

A 95% confidence interval for population proportion p is ,

± E   

= 0.36  ± 0.094

=( 0.266, 0.454 )

We are 95% confident that the true proportion of helmets that would sustain damage in this testing between 0.266 and 0.454.