Question

The technology underlying hip replacements has changed as these operations have become more popular (over 250,000 in the United States in 2008). Starting in 2003, highly durable ceramic hips were marketed. Unfortunately, for too many patients the increased durability has been counterbalanced by an increased incidence of squeaking. An article reported that in one study of 146 individuals who received ceramic hips between 2003 and 2005, 11 of the hips developed squeaking.

(a) Calculate a lower confidence bound at the 95% confidence level for the true proportion of such hips that develop squeaking. (Round your answer to three decimal places.)

Answer 1

Solution :

Given that,

n = 146

x = 11

Point estimate = sample proportion = = x / n = 11 / 146 = 0.075

1 - = 1 - 0.075 = 0.925

At 95% confidence level

= 1 - 95%

=1 - 0.95

= 0.05

Z = Z0.05  = 1.645

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

= 1.645 (((0.075 * 0.925) / 146 )

= 0.036

A 95% lower confidence interval for population proportion p is ,

- E < p

= 0.075 - 0.036 < p

lower confidence interval = 0.039 < p