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T-test and P-Value

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Solar cells are attached to a panel with a new heat resistant adhesive. The adhesive must provide 2.80 pounds of force in order to hold the cell on the panel. A random sample of 50 cells is tested and the following forces are necessary to break the adhesive.

2.65 2.76 2.82 2.89 2.95
2.67 2.77 2.83 2.90 2.95
2.68 2.77 2.84 2.90 2.97
2.68 2.77 2.84 2.91 2.98
2.70 2.78 2.84 2.92 2.98
2.70 2.78 2.85 2.92 2.99
2.73 2.79 2.88 2.93 3.00
2.74 2.80 2.88 2.93 3.01
2.75 2.81 2.88 2.93 3.02
2.75 2.82 2.89 2.94 3.03

(a) Test at the 0.01 level of significance the hypothesis that the mean adhesive strength is at least 2.80 pounds.
(b) Assuming the data follow a normal distribution, what proportion of the cells would you estimate to be out of tolerance(i.e., less than 2.80 pounds of adhesive strength)?
(c) Discuss your results from part a and b above. Is a test for the mean appropriate in this case? Why or why not?

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