The following reaction times (measured to the nearest second) were recorded for 8 drivers under two different conditions, without consuming alcohol and after consuming a controlled amount of alcohol.

Question

Pls show the solution step by step.

The following reaction times (measured to the nearest second) were recorded for 8 drivers under two different conditions, without consuming alcohol and after consuming a controlled amount of alcohol.

Driver	1	2	3	4	5	6	7	8
Without Alcohol	3	4	3	3	6	5	3	5
With Alcohol	3	5	4	6	7	4	4	7

(a)  Test, at 1% level of significance, whether there is evidence that the alcohol  increases the reaction time .(12 marks)

(b) Do you think it is necessary to use the same driver for two different conditions above? Explain your reasoning. (3 marks)

Answer 1

part A:

without alcohol, the mean average is 4 and

the standard deviation is 1.195229

with alcohol, the mean average is 5 and

the standard deviation is 1.511858

(I can show you the steps for getting the variance

and standard deviation, but I used MS Excel)

the numerator of the test statistic is simply the

difference of the means, which is 1.

the denominator is more complicated: sqrt[ stndDev1^2/N1 + stndDev2^2/N2]

= sqrt [ 1.195229^2/8 + 1.511858^2/8]

= sqrt [ 0.464285871825625]

=0.68138525947192679198926220313399

the reciprocal of this is the test statistic value,

which is 1.467598....

at 1%, the statistical evidence supports the hypothesis that

there is NO difference between the average reaction times

part B :

"CONTROLLED" amount of alchohol..... is it above the legal amount???

Using two different drivers may be a factor because each person

has different reactions to the alcohol.