For each hypothesis test please give the following information:
(a) Describe the null hypothesis and the alternate hypothesis.
(b) Determine the sampling distributions to be used; find the critical value(s).
(c) Draw the critical region and describe the critical values(s) on the sketch.
(d) Calculate the test statistics and show its location on the sketch of part (c).
(e) Based upon your answers to parts (a) through (d) decide whether to reject or fail to reject the null hypothesis at the given level of significance. Discuss your conclusion in simple terms (English)
The Food and Drug Administration has approved a prescription medication that contains 4 mg. of codeine per pill. To determine if the pills actually contain 4 mg. of codeine, a random sample of 16 pills were analyzed. The mean codeine content was 3.8 mg. with sample standard deviation 0.4 mg. Test the hypothesis that the actual codeine content of the pills is less then 4 mg. Use a 1% level of significance. Assume that the production of the pills is such that the amount of codeine per pill follows a normal distribution.