A study conducted by a commuter train transportation authori

A study conducted by a commuter train transportation authority involved surveying a random sample of 200 passengers. The results show that a customer had to wait on the average 9.3 minutes with a standard deviation of 6.2 minutes to buy his or her ticket. Construct a 95% confidence interval for mu, the true mean waiting time. What is the lower confidence limit?

Solution

Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=9.3
Standard deviation( sd )=6.2
Sample Size(n)=200
Confidence Interval = [ 9.3 ± t a/2 ( 6.2/ Sqrt ( 200) ) ]
= [ 9.3 - 1.972 * (0.438) , 9.3 + 1.972 * (0.438) ]
= [ 8.435,10.165 ]