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Test at a = .05 if there is a significant difference in the measurements obtained with the two methods.

For question 4 , assume that independent simple random samples are taken from normal distributions. 4.The Rockwell index of hardness for steel is determined by pressing a diamond point into steel and measuring the depth of penetration. The Rockwell hardness for random samples of two types of steel was measured, yielding the following results:

Type I 66 60 69 74 75

Type II 79 68 80 73 69 72

(a) Use the Pooled T-test to test at  = .05 if there is a significant difference in the mean Rockwell hardness for the two types of steel.

(b) Estimate the average difference in Rockwell hardness for the two types of steel using a 95% confidence interval.

(c) Which type of steel, if any, is harder on average? Explain using the confidence interval in (b).