Question

It was believed from the experiment on the obstacle course, in Part I, that there is a relationship between a subject’s reaction time before drinking two beers and the subject’s age:

Experiment carried out in part I

Drunk driving is one of the main causes of car accidents. Interviews with drunk drivers who were involved in accidents and survived revealed that one of the main problems is that drivers do not realise that they are impaired, thinking “I only had 1-2 drinks … I am OK to drive.” A sample of 5 drivers was chosen, and their reaction times (seconds) in an obstacle course were measured before and after drinking two beers. The purpose of this study was to check whether drivers are impaired after drinking two beers. Below is the data gathered from this study

Driver 1 2 3 4 5

Before 6.15 2.86 4.55 3.94 4.19

After 6.85 4.78 5.57 4.01 5.72

Driver 1 2 3 4 5

Age (years) 20 30 25 27 26 1.

(a)What type of study is being outlined here? Justify your answer?

(b)Plot a graph representing the relationship between reaction times before drinking two beers and age.

(c) From the graph in (b), suggest a relationship that could exist between the two measurements?

(d)Use a 1% level of significance and the following points to test the claim that there is a relationship between the reaction times before drinking two beers and age.

(i) State the null and alternative hypotheses in context

.(ii) Calculate the test statistic.

(e) Identify the rejection region(s).

(f) Clearly state your conclusions (in context).

(g)What percentage of variation in reaction times before drinking two beers is unexplained by the relationship between reaction times before drinking two beers and age?

(h) Derive a model/equation that could be used to predict reaction times before drinking two beers for a person, if the age of the person is known.

(i) Using the model derived in (h), what would the predicted reaction time, in the obstacle course, before drinking two beers of a 22-year-old be?

Answer 1

(a) The two measurements are dependent because data comes from natural pairing (same person's age and reaction time).

(b) Enter data in excel.

Select whole data and click on Insert->Scatterplot->Select first Scatterplot.

The scatterplot is shown below:

(c) Overall pattern moves from upper left to lower right, there seems negative association between variables.

(d) Click on Data->Data Analysis->Regression.

In Y variable, enter Before data range with label.

In X variable, enter Age data range with label.

Check Label and click OK.

i) The null and alternative hypotheses are:

H0: There is no relationship between the reaction times before drinking two beers and age

Ha: There is a relationship between the reaction times before drinking two beers and age

ii) The test statistic is F = 2830.93

(e) From F table, critical value of F is F_1,3 > 34.12. Therefore, the rejection region is, F > 34.12.

(f) Since test statistic falls in critical region, reject the null hypothesis.

(g) From above output, R-square = 0.9989

Unexplained variation = 1 - R-square = 1 - 0.9989 = 0.0011 = 0.11%

(h) From above output, using coefficient column, the regression equation is:

(i) The predicted reaction time, in the obstacle course, before drinking two beers of a 22-year-old be: