Question

Researchers tested the strength of three brands of trash bags. One pound weights were placed into a bag, one at a time, until the bag broke. The completed ANOVA table is below. The F-test revealed significant evidence that not all bags have equal strength.

The following indicates the average amount of weight placed in each bag brand before it broke. Perform the LSD method to determine which bags are significantly different. Use alpha 0.05.

Hefty = 34.0 pounds

Glad = 35.6 pounds

Kroger = 29.9 pounds

If 100 Hefty bags cost $2.99, and 100 Glad bags cost $3.49, and 100 Kroger bags cost $2.99, which bags should you buy? Be specific. Think about BOTH cost and strength.

Source            DF      SS          MS                     F

treatment        2          486        243                    16.2

Error               27         405        15

Total               29         891         

Answer 1

LSD = t*MSE*(1/n1 + 1/n2)

LSD = 2.05*15*(1/10 + 1/10)

LSD = 3.55

Mean difference between Hefty and Glad = 35.6 - 34 = 1.6

Since 1.6 < 3.55, there is no significant difference between Hefty and Glad.

Mean difference between Hefty and Kroger = 34 - 29.9 = 4.1

Since 4.1 > 3.55, there is a significant difference between Hefty and Kroger.

Mean difference between Glad and Kroger = 35.6 - 29.9 = 5.7

Since 5.7 > 3.55, there is a significant difference between Glad and Kroger.

Since there is no significant difference between Hefty and Glad bags, we should buy the less expensive one to save cost.

Thus, 100 Heft bags should be bought for $2.99 since they can hold a huge amount of weight and are also less expensive than the other bags.