Refer to Exercise 2.34, page 46, concerning the number of board failures for \(n=32\) integrated circuits. A computer calculation gives \(\bar{x}=7.6563\) and \(s=\) 5.2216. At the 0.01 level of significance, conduct a test of hypotheses with the intent of showing that the mean is greater than 7 .

Data From Exercise 2.34

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2.34 A contract for the maintenance of a leading manufac- turer's computers was given to a team of specialists. After six months, the supervisor of the team felt that computer performance could be improved by modify- ing the existing IC board. To document the current sta- tus, the team collected data on the number of IC board failures. Use the data below to: (a) calculate the sample mean x, (b) calculate the sample standard deviations. Number of IC board failures: 12 3 8 6 19 1 25 1 11 14 3 13 2 98 24 1 4 13 3 11 9 15 14 5 12 7 6 16 10 0