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A quality engineer wants to decide if the defect rate of a manufacturing process exceeds 0

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A quality engineer wants to decide if the defect rate of a manufacturing process exceeds 0.1. In a random sample of 85 production parts manufactured by this process, 10 are found to be defects. Formulate the engineer's decision-making problem as a hypothesis testing problem. Specifically, (a) State the hypotheses and test them using a significance level of 0.05. (b) If the true defect rate of this manufacturing process is 0.15, how likely is it that the test procedure in part (a) will not reject the null hypothesis? (c) If the true defect rate of this manufacturing process is 0.15, how large would the sample size have to be for the engineer to correctly reject the hypothesized defect rate of 0.1 with a probability of 0.9? Notes: (1) Note that no mathematical symbol is used in the problem description, so you have to clear define any mathematical symbol that you decide to use in your answer. (2) Elaborate your answers so that the arguments are easy to follow, and the calculations are easy to repeat and verify.