Question

12. In a sample of 133 hip surgeries of a certain type, the average surgery time was 130.2 minutes with a standard deviation of 24.6 minutes. Construct a 90% confidence interval for the mean surgery time for this procedure and interpret your result. Round your answer to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$= 130.2

Population standard deviation =   $\sigma$ =24.6
Sample size = n =133

At 90% confidence level

$\alpha$ = 1 - 90%  

$\alpha$ = 1 - 0.90 =0.10

$\alpha$/2 = 0.05

Z$\alpha$/2 = Z0.05 = 1.645

Margin of error = E = Z/2    * ( $\sigma$ /$\sqrt$n)

= 1.645* ( 24.6 /  $\sqrt$133 )

= 3.5
At 90% confidence interval estimate of the population mean
is,

$\bar x$ - E < $\mu$ < $\bar x$ + E

130.2 - 3.5 <  $\mu$ <   130.2+ 3.5

126.7 <  $\mu$ < 133.7

( 126.7 , 133.7 )