Question

Travel time data is collected on an arterial. With 30 runs, an average travel time of 152 seconds is computed over the 2.0 miles length, with a computed standard deviation of 17.3 seconds.

Required:
a. Compute 95% confidence bounds on your estimate of the mean.
b. Was it necessary to make any assumption about the shape of the travel-time distribution?

Answer 1

a

The 95% confidence bounds is
`145.80 <  \mu <   158.19`

b

It was not necessary to make any assumption about the shape of the travel time distribution

Explanation:

From the question we are told that

The sample size is n = 30

The sample mean is
`\=x = 152`

The standard deviation is
`\sigma = 17.3 \ second`

From the question we are told the confidence level is 95% , hence the level of significance is

`\alpha = (100 - 95 ) \%`

=>
`\alpha = 0.05`

Generally from the normal distribution table the critical value of
`(\alpha )/(2)` is

`Z_{(\alpha )/(2) } =  1.96`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } *  (\sigma )/(√(n) )`

=>
`E =  1.96 *  (17.3 )/(√(30) )`

=>
`E = 6.19`

Generally 95% confidence bounds is mathematically represented as

`\= x -E <  \mu <  \=x  +E`

=>
`152  -6.19 <  \mu <  152  -6.19`

=>
`145.80 <  \mu <   158.19`

This 95% confidence bounds show that there is 95% confidence that the true mean lies within this bound hence there is it was not necessary to make any assumption about the shape of the travel time distribution