A plant superintendent has been assigned the task of improving the joint strength of a clutch assembly. The assembly consists of two components: the clutch cup and the drive sprocket. The two components are joined together by means of a brazing operation. The plant superintendent wanted to investigate whether changing the brazing material would affect average braze strength. They decided he would braze one group with pure copper wire and braze another group with the existing copper alloy. One of the two components, the sprocket, is manufactured from powdered metal. The superintendent had observed from past studies that there was a strong relationship between the density of the sprocket and the joint strength of the assembly after brazing. The greater the porosity of the powdered metal sprocket, the more absorption of the braze material takes place, resulting in a weaker bond. They decided to use the known relationship between sprocket porosity and joint strength for setting up a matched-pairs design. 100 sprockets were randomly selected from inventory and identified and measured for density. They were then rank ordered from lowest to highest and paired according to their density. Each pair of sprockets was randomly assigned to one of two groups that were to receive the different brazing material. Once the random assignments were completed, the superintendent verified that there was no statistically significant difference between the two groups for density in terms of central tendency and dispersion. The two groups were then run in pairs through the braze furnace. The braze strength of the assemblies was tested to failure in the laboratory on an Instron machine. The superintendent calculated the following statistics:

Copper Alloy

Mean1 = 3671 lbs

s1 = 246 lbs

n2 = 50 (pairs)

Pure Copper

Mean2 = 4228

s2 = 182 lbs

r12 = 0.78

Test an appropriate hypothesis using an alpha = 0.05.

A. What is the source of the dependency?

-Matching

-Subdividing a homogenous unit

-Repeated measure

-Pairing (natural or artificial)

B. What is the value of the proper test statistic? Record your answer to three places after the decimal point (e.g. X.XXX).

C. What is your decision with respect to the Null Hypothesis, H0: 1- 2 = 0?

- Reject the Null Hypothesis

- Accept / Fail to Reject the Null Hypothesis