statistic assignment

(a) The average tablet weight is 501 mg with a standard deviation of 5.3. A new batch shows the following weights of six tablets: 500, 499, 493, 497, 504 and 495 mg .Does the new batch have a different mean from the average?

(b) Two batches of the tablets were prepared by two different processes.
Batch A: 5.1, 4.9, 4.6, 5.3, 5.5, 4.7.
Batch B: 4.8, 4.8, 5.2, 5.0, 4.5.,4.4.
Test to see if the means of the two batches are equal.

(c) What is the answer to part (a) if the variance was unknown. Place a (i) 95% and (ii) 99% confidence interval on the true average weight.