A pharmaceutical company produces pills of dose level of 40 mg. To maintain the quality control, the average weight of all pills needs to be 40 mg and the st. dev. 0.4 mg. A sample of 25 pills yielded...

A pharmaceutical company produces pills of dose level of 40 mg. To maintain the quality control, the average weight of all pills needs to be 40 mg and the st. dev. 0.4 mg. A sample of 25 pills yielded the sample mean of 39.5 mg. Test the hypothesis at  that the average weight of the pills has changed. Assume that the weights of the pills follow normal distribution. You must state the null and the alternative hypotheses.