7.8 The mean pH value of a certain chemical is to be controlled at 5. Deviation from this target value in either direction is to be detected with high probability. For this purpose it is proposed to measure a certain number of samples from each batch and decide that the mean pH is different from 5 if the sample mean differs significantly from 5 at the 10% level of significance. (a) State the hypotheses tested by the above decision rule. Interpret the test parameter M. (b) What sample size is needed if the probability of not detecting a change of one standard deviation is to be no more than 1%? (c) Suppose that 16 samples are measured. The sample mean (9 is 4.915 and the sample standard deviation 5 is 0.2. Ignoring that we have a small sample and assuming that 5 ~ 0, calculate the P-value. Do you conclude that the mean pH has changed from the target value of 5? Use a = 0.10