Question

The waiting time (in minutes) at a bus stop has exponential distribution with mean >0. The waiting times on ten occasions were recorded as follows:

6.2, 5.8, 4.5, 6.1, 4.6, 4.8, 5.3, 5.0, 3.8, 4.0

a. Construct a 95% two-sided confidence interval for the true average waiting time.

b. Construct a 95% two-sided confidence interval for the true variance of the waiting time.

Answer 1

	Values ( X )
	6.2	1.4161
	5.8	0.6241
	4.5	0.2601
	6.1	1.1881
	4.6	0.1681
	4.8	0.0441
	5.3	0.0841
	5	0.0001
	3.8	1.4641
	4	1.0201
Total	50.1	6.269

Mean

Standard deviation

Part a)

Confidence Interval



Lower Limit =
Lower Limit = 4.413
Upper Limit =
Upper Limit = 5.607
95% Confidence interval is ( 4.413 , 5.607 )

part b)

\alpha = 0.05
n = 10




Lower Limit =
Upper Limit =
95% Confidence interval is ( 0.3296 , 2.3217 )
( 0.3296 < < 2.3217 )