Question

Students in a business statistics course performed a completely randomized design to test the strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until the bag broke. A total of 40 bags, 10 for each brand, were used. The data in give the weight (in pounds) required to break the trash bags. Dataset: Trashbags

1. At the 0.05 level of significance, is there evidence of a difference in the mean strength of the four brands of trash bags?
2. If appropriate, determine which brands differ in mean strength.
3. At the 0.05 level of significance, is there evidence of a difference in the variation in strength among the four brands of trash bags?

   Kroger	Glad	Hefty	TuffStuff
   34	32	33	26
   30	42	34	18
   40	34	32	20
   38	36	40	15
   36	32	40	20
   30	40	34	20
   30	36	36	17
   42	43	34	18
   36	30	32	19
   38	38	34	20

Answer 1

(a) The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	3	1986.5	662.16	48.11	0.000
Error	36	495.5	13.76
Total	39	2482.0

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference in the mean strength of the four brands of trash bags.

(b) Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
Glad	10	36.30	A
Kroger	10	35.40	A
Hefty	10	34.900	A
TuffStuff	10	19.300		B

Means that do not share a letter are significantly different.

(c) The hypothesis being tested is:

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

Test

Method	Test Statistic	P-Value
Multiple comparisons	—	0.576
Levene	1.46	0.242

The p-value is 0.242.

Since the p-value (0.242) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that there is no difference in the variation in strength among the four brands of trash bags.