An engineer measured the Brinell hardness of 25 pieces of ductile iron from her company, that were subcritically annealed. She believes that the alloys her company uses in iron, will ultimately make the iron stronger, and thus will have a higher Brinell hardness score. She tests 25 pieces of ductile iron from her company with the resulting data of Brinell hardness scores:

170 167 174 179 179 187 179 183 179
156 163 156 187 156 167 156 174 170
183 179 174 179 170 159 187

The engineer hypothesizes that the mean Brinell hardness score of such ductile iron pieces from her company will greater than known average Brinell score for iron which is 170. At the 5% level of significance, is there enough evidence to conclude this?

State the Claims which means to State the null and alternative hypotheses. Use correct math type. You may want to consider looking back at the symbols assignment from the beginning of class.

a. What is the sample mean?
b. What is the sample standard deviation?
c. Are the normality assumptions met?
d. Conclusion. State your conclusion. Either reject or fail to reject H0 , indicate why, then write the conclusion in terms of the problem.