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The Rockwell hardness index for steel is determined by pressing a diamond point into the steel and measuring the depth of the penetration. Below are the Rockwell hardness indices for a random sample of 25 specimens of a particular type of steel. (Note: data values have been sorted below to help calculations)

46 51 54 56 56 57 59 59 60 60 65 65

66 67 68 69 69 70 71 72 73 74 74 76 79

The manufacturer claims that the "average" Rockwell hardness index for this type of steel exceeds 60. Determine if there is sufficient evidence to support the manufacturer's claim. (a = 0.01)

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