please show all workout step by step with appropriate formula used and full explanation.

Statistics question.

I Tables . Pana R10. A random sample of size 50 yielded a mean of 21 and a standard deviation of 10. By Construct a 95% confidence interval for the population mean . b ) Test Ho: M = 20 against Ha: Mu # 20 (Use CK)= 0.05.) C) Test Ho: M = 19 against Ha: / # 19 (Used()= 0.05.) d) With reference to part (a) explain the apparent contradiction in your answers to parts (b) and (c)