Question

In a random sample of 94 bicycle wheels, 44 were found to have critical flaws that would result in damage being done to the bicycle. Determine the lower bound of a two-sided 95% confidence interval for p, the population proportion of bicycle wheels that contain critical flaws. Round your answer to four decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 44 / 94 = 0.4681

Z_/2 = 1.96

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

= 1.96 * (((0.4681 * 0.5319) / 94)

= 0.1009

The lower bound of a two-sided 95% confidence interval for p is

+ E = 0.4681 - 0.1009 = 0.3672