Refer to Exercise 8.14. Test with \(\alpha=0.01\), that the mean difference is 0 versus a two-sided alternative.

Data From Exercise 8.14

Find a 99% confidence interval for the mean difference in machine readings assuming the differences have a normal distribution.

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8.14 A civil engineer wants to compare two machines for grinding cement and sand. A sample of a fixed quantity of cement and sand is taken and put in each machine. The machines are run and the fine- ness of each mixture is noted. This process is re- peated five times. The results, in microns, are as follows: Sample No. 1 2 3 4 5 Machine A Machine B 35369 7968 + 4