Question

An article reports that in a sample of 123 hip surgeries of a certain type, the average surgery time was 136.9 minutes with a standard deviation of 22.9 minutes.

(A) Find a 98% lower confidence bound for the mean time. Round the answer to two decimal places.

(B) Someone says that the mean time is greater than 134.26 minutes. With what level of confidence can this statement be made? Express the answer as a percent and round to two decimal places.

Answer 1

a)

sample std dev ,    s =    22.9000
Sample Size ,   n =    123
Sample Mean,    x̅ =   136.9000

Level of Significance ,    α =    0.02          
degree of freedom=   DF=n-1=   122          
't value='   tα/2=   2.3573   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   22.900   / √   123   =   2.0648
margin of error , E=t*SE =   2.3573   *   2.065   =   4.867
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    136.90   -   4.867   =   132.03

b)

given that

x̅ - E =134.26

E = 136.9-134.26 = 2.64

E=t*SE = t *   2.065 = 2.64

t(α/2) = 2.64/2.065 = 1.2784

α=0.2035

confidence level = 1-0.2035 = 0.7965

so, answer: 79.65%