Question

(Please answer without using MINITAB)

Police cars, ambulances, and other emergency vehicles are required to carry road flares. One of the most important features of flares is their burning times. To help decide which of four brands on the market to use, a police laboratory technician measured the burning time for a random sample of 10 flares of each brand. The results were recorded to the nearest minute.

a. Can we conclude that differences exist between the burning times of the four brands of flares?

b. Apply Fisher’s LSD method with the Bonferroni adjustment to determine which flares are better.

c. Repeat Part b using Tukey’s method.

DATA

Flare A	Flare B	Flare C	Flare D
51	45	58	60
66	61	71	35
76	48	64	59
60	57	59	50
51	49	67	55
58	72	60	48
59	55	60	54
71	58	60	41
71	65	64	53
53	63	55	63

Answer 1

The analysis is carried out in R and the results are below.
1. The test hypotheses are
H0 : Null hypothesis : The group means are same
H1 : alternative Hypothesis : The group means are not same.

Anova output

The p value < 0.05, So we reject the null hypotheis. So we can conclude that differences exist between the burning times of the four brands of flares.

b) Fisher’s LSD method with the Bonferroni adjustment

c) using Tukeys method

The groups D-C and D-A are showing signifiacnt difference.
The boxplot is below