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

Answer:

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:

$\bar X = \frac{1.2+1.8}{2}= 1.5$

And the margin of error is given by:

$ME = \frac{1.8-1.2}{2}= 0.3$

Step-by-step 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:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$   (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:

$\bar X = \frac{1.2+1.8}{2}= 1.5$

And the margin of error is given by:

$ME = \frac{1.8-1.2}{2}= 0.3$