Question

Experience    RoadType Correction Time
Beginner Paved 4
Beginner Paved 18
Beginner Paved    8
Beginner Paved 10
Beginner Gravel    23
Beginner Gravel    15
Beginner Gravel    21
Beginner Gravel    13
Beginner Dirt    16
Beginner Dirt    27
Beginner Dirt    23
Beginner Dirt    14
Advanced    Paved    6
Advanced    Paved    4
Advanced    Paved 13
Advanced    Paved    7
Advanced    Gravel 2
Advanced    Gravel 6
Advanced    Gravel 8
Advanced    Gravel    12
Advanced    Dirt    20
Advanced    Dirt    15
Advanced    Dirt 8
Advanced    Dirt    17

1.      [MiniTab] The file RoadConditions.MTW contains data on the time it takes drivers to make steering corrections based on the drivers’ experience level (advanced or beginner) and the road type (paved, gravel, or dirt). Use this data to answer the following questions.

A)    Test the hypothesis that the average time it takes drivers to make steering corrections is different based on the road type being driven on. Report your hypotheses, test statistic, and p-value.

B)    What would be your conclusion if you tested this hypothesis at α = 0.05?

C)    What would be your conclusion if you tested this hypothesis at α = 0.01?

   

Answer 1

One-way ANOVA: correction time versus Road

Method

Null hypothesis         All means are equal
Alternative hypothesis At least one mean is different
Significance level      α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Road         3 Dirt, Gravel, Paved

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Road     2   308.3 154.17     4.25    0.028
Error   21   761.5   36.26
Total   23 1069.8

Ha : not ()

TS = F = 4.25 , p-value = 0.028

b)

if p-value < alpha , we reject the null hypothesis , otherwise we fail to reject the null hypothesis

here p-value = 0.028 < 0.05

hence we reject the null hypothesis

we conclude that there is difference between different type of roads

c)

p-value > 0.01

then we will fail to reject the null hypothesis

we conclude that there is not difference in different type of road