Question

An industrial wind turbine is designed to produce a maximum of 18 MW of power in a 60 km/h wind. Lab tests of 120 turbines showed that seven did not meet this standard.  

a) Determine the margin of error at a 95% confidence level.

b) Determine a 95% confidence interval for the proportion of turbines from the plant that do not meet the standard.  

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 7 / 120 = 0.058

1 - = 1 - 0.058 = 0.942

Z/2 = Z0.025 = 1.96

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

= 1.96 (((0.058 * 0.942) / 120)

= 0.042

b) A 95% confidence interval for population proportion p is ,

± E

0.058 ± 0.042

(0.016 , 0.100)