Question

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 = = 130.2

Population standard deviation =    = 24.6
Sample size = n =133

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2    * ( /n)

= 1.645* (24.6 /  133 )

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

- E < < + E

130.2 -3.5 <   <130.2 + 3.5

126.7<   < 133.7

(  126.7, 133.7 )