Question

in a study of thermal annealing process, hardness of steel is measured before annealing and after annealing. a group of 16 samples measured and the test results are given in the table below

before ann 209 178 169 212 180 192 158 180 170 153 183 165 201 179 243 144

after ann 196 171 170 207 177 190 159 180 164 152 179 162 199 173 231 140

1. Use the .01 level of significance to test whether the annealing process is effective
2. Estimate the p-value

Answer 1

Before	After	Difference
209	196	13
178	171	7
169	170	-1
212	207	5
180	177	3
192	190	2
158	159	-1
180	180	0
170	164	6
153	152	1
183	179	4
165	162	3
201	199	2
179	173	6
243	231	12
144	140	4
	Total	66

Claim: The annealing process is effective.

The null and alternative hypothesis is

Level of significance = 0.01

Sample size = n = 16

Sample mean of difference = = 4.125

Sample standard deviation of difference = = 4.0641

Test statistic is

Degrees of freedom = n - 1 = 16 - 1 = 15

P-value = P(T > 4.06) = 0.0005

P-value < 0.01 we reject null hypothesis.

Conclusion:

The annealing process is effective.