Question 11 [WSRT] The Rockwell hardness index for steel is determined by pressi

Question

Question 11 [WSRT]

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.

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. ( = .01)

Explanation / Answer

Data:     

n = 25    

= 60    

s = 8.47    

x-bar = 64.64    

Hypotheses:     

Ho: 60    

Ha: > 60    

Decision Rule:     

= 0.01    

Degrees of freedom = 25 - 1 = 24   

Critical t- score = 2.492159469    

Reject Ho if t > 2.492159469    

Test Statistic:     

SE = s/n = 8.47/25 = 1.694   

t = (x-bar - )/SE = (64.64 - 60)/1.694 = 2.739079103   

p- value = 0.005716087    

Decision (in terms of the hypotheses):     

Since 2.739079103 > 2.492159469 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence that the average hardness exceeds 60.

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