A drug mаnufаcturer prоduces аn antibiоtic in large fermentatiоn vats (containers). To determine the average potency for the batch of antibiotic being prepared, the vat is sampled at 9 randomly selected locations. The 9 potency readings have the mean of 8.7 and the standard deviation of 0.36. The sample data are obtained using simple random sampling. Also, assume that the potency readings follow a normal distribution. a) Construct a 95% confidence interval estimate for the population mean potency reading for the vat. Also interpret the confidence interval. b) The target potency level for this antibiotic is to be 9.0. Use the confidence interval in part (a) to answer the following question and explain how you determined your answer. “Is there evidence at 5% significance level to say the mean potency level for this vat differs from 9.0?” Explain.