Question

A study is conducted to determine the extent to which drinking alcohol impairs driving ability. Forty volunteers are each tested twice on a computer simulated driving course, once while sober and once while intoxicated. The tests took place over two days and the order of the treatments were randomly assigned to each volunteer. One of the variables measured is the response time (in seconds) to a certain stimuli. The mean difference in response times measured while intoxicated versus sober is 0.914 seconds with standard deviation 1.496 seconds. Calculate the 99% confidence interval for the mean difference between the response times measured while intoxicated versus sober. Use t*

Answer 1

The 99% confidence interval for the mean difference between the response times measured while intoxicated versus sober is between 0.274 and 1.554 seconds.

Explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 40 - 1 = 39

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.99)/(2) = 0.995`. So we have T = 2.7079

The margin of error is:

`M = T(s)/(√(n)) = 2.7079(1.496)/(√(40)) = 0.64`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 0.914 - 0.64 = 0.274 seconds

The upper end of the interval is the sample mean added to M. So it is 0.914 + 0.64 = 1.554 seconds

The 99% confidence interval for the mean difference between the response times measured while intoxicated versus sober is between 0.274 and 1.554 seconds.