12 The customer service department of a local gas utility wa

12. The customer service department of a local gas utility wants to estimate the average length of time between the entry of the service request and the connection of service. A random sample of 10 houses is selected from the records available during the past year. The results recorded in number of days are as follows.

114         78             96             137           78             103           117           126           86             99

Assuming the distribution of time as normal, construct a 95% confidence interval estimate of the average length of time (m)

I really need help for this question!!

Solution

sample mean=103.4

sample standard deviation=20.01222

The degree of freedom =n-1=10-1=9

Given a=1-0.95=0.05, t(0.025, df=9)=2.26 (from student t table)

So the lower bound is

xbar -t*s/vn=103.4-2.26*20.01222/sqrt(10) =89.09777

So the upper bound is

xbar +t*s/vn=103.4+2.26*20.01222/sqrt(10) =117.7022