# Investigation whether people react more quickly to hazards when cycling during the day than at night

A student would like to investigate the assumption that people react more quickly to hazards when cycling during the day than at night. For this purpose, he measures the reaction time (in seconds) of five other students (i ∈ {1, . . . , 5}) to a traffic light changing from green to red at night (Let the random variable for the reaction time at night be X) and during the day (let the random variable for the reaction time during the day is Y)

The table is as the following

Students | 1 | 2 | 3 | 4 | 5

Xi | 1.9 | 2.8 | 2.1 | 2.7 | 2.3

Yi | 2.0 | 2.5 | 1.5 | 2.2 | 1.8

Can the assumption be confirmed on the basis of the available data at a significance level of α = 0.05? To do so, use a distribution-free test and state the associated hypotheses. Calculate the test statistic analytically and make the test decision on the basis of these.

The student wishes to use a parametric test in the following.

(i) Specify an appropriate parametric test and the associated hypotheses that

the student can use. Include a discussion of the assumptions needed.

(ii) Assume below that the assumptions from subtask (i) are met.

Perform the test from subtask (i) analytically. Calculate the test statistic and use it to make your test decision