Question

The authors of a certain paper describe a study to evaluate the effect of mobile phone use by taxi drivers in Greece. Fifty taxi drivers drove in a driving simulator where they were following a lead car. The drivers were asked to carry on a conversation on a mobile phone while driving, and the following distance (the distance between the taxi and the lead car) was recorded. The sample mean following distance was 3.80 meters and the sample standard deviation was 1.19 meters.

Construct a 95% confidence interval (in meters) for μ, the population mean following distance while talking on a mobile phone for the population of taxi drivers. (Round your answers to three decimal places.)

Answer 1

The 95% confidence interval is
`3.462 <  \mu <  4.138`

Explanation:

From the question we are told that

The sample size is n = 50

The sample mean is
`\=  x =  3.80`

The standard deviation is
`\sigma  =  1.19`

Given that the confidence level is 95% then the level of confidence is mathematically represented as

`\alpha =  (100 - 95)\%`

=>
`\alpha =  0.05`

Generally from the t distribution table the critical value of
`(\alpha )/(2)` at a degree of freedom of
`df =  50 -1 = 49` is

`t_{(\alpha )/(2) ,49 } =  2.0096`

Generally the margin of error is mathematically represented as

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

=>
`E =2.0096 *  (1.19)/(√( 50) )`

=>
`E = 0.3381`

Generally 95% confidence interval is mathematically represented as

`\= x -E <  \mu <  \=x  +E`

`3.80 -0.3381 <  \mu <  3.80 +0.3381`

=>
`3.462<  \mu <  4.138`