# Fisher's LSD approach and the posttest model

1. The Cordage Institute, based in Wayne, Pennsylvania, is an international association of manufacturers, producers, and resellers of cordage, rope, and twine. It is a not-for-profit corporation that reports on research concerning these products. Although natural fibers like manila, sisal, and cotton were once the predomonant rope materials, industrial synthetic fibers dominate the marketplace today, with most ropes made of nylon, polyester, or polypropylene. One of the principal traits of rope material is its breaking strength. A research project generated data giving the file entitled KNOTS. The data listed were gathered on 10 different days from 1/2" diameter ropes.

a) Test to determine if inserting the day on which the testing was done was necessary. Use a significance level of

0.05

b) Based on the data gathered by the Cordage Institute, can it be concluded that there is a difference in the average

breaking strength of nylon, polyster, and polypropylene?

c) If you concluded that there was a difference in the average breaking strength of the rope material, use Fisher's

LSD approach to determine which material has the highest breaking strength

2. When the world's largest retailer, Walmart, decided to enter the grocery marketplace in a big way with its "Super Stores," it changed the retail grocery landscape in a major way. The other major chains such as Albertsons have struggled to stay competative. In addition, regional discounters such as WINCO in the western United States have made it difficult for the traditional grocery chains. Recently, a study was conducted in which a "market basket" of producers was selected at random from those items offered in three stores in Boise, Idaho: Walmart, WINCO, and Albertsons. At issue was whether the mean prices at the three stores are equal or whether there is a difference in prices. The sample data are in the data filed called FOOD PRICE COMPARISONS. Using an alpha level equal to 0.05, test to determine whether the three stores have equal population mean prices. If you conclude that there are differences in the mean prices, perform the appropriate posttest to determine which stores have different means.

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#### Solution Preview

1. a) By running "correlation" under "data analysis", we could obtain the following correlation matrix:

Day Strength

Day 1

Strength -0.07165 1

Therefore, r = -0.07165

Null hypothesis: r = 0

Alternative hypothesis: r ≠ 0

The degree of freedom is 30 - 2 = 28

At 0.05 significance level, the critical t values are ±2.048

Test value t = r*sqrt((n-2)/(1-r^2)) = -0.07165*sqrt((30-2)/(1-0.07165^2)) = -0.380

Since -2.048 < -0.380 < 2.048, we could not reject null hypothesis.

Therefore, inserting the day was not necessary.

b) After running "ANOVA: single factor", we could obtain the following ...

#### Solution Summary

The expert examines Fisher's LSD approach and the posttest model.