Question

A researcher studying reaction time of drivers states that, "A 95% confidence interval for the mean time (8.1) it takes for a driver to apply the brakes after seeing the brake lights on a vehicle in front of him is 1.2 to 1.8 seconds. What are the point estimate and margin of error for this interval?

Answer 1

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for
`\mu` would be:

`\bar X = (1.2+1.8)/(2)= 1.5`

And the margin of error is given by:

`ME = (1.8-1.2)/(2)= 0.3`

Explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

`\bar X` represent the sample mean for the sample

`\mu` population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

`\bar X \pm t_(\alpha/2)(s)/(√(n))` (1)

For this case we know that the confidence interval is given by (1.2 , 1.8) and the point of estimate for
`\mu` would be:

`\bar X = (1.2+1.8)/(2)= 1.5`

And the margin of error is given by:

`ME = (1.8-1.2)/(2)= 0.3`