The management of a manufacturing company has been tracking the performance of two different machines in terms of their production output. The company collected the following data over a period of 15 days:

Machine A: nA = 15, x?A = 120 units, sA = 5 units
Machine B: nB = 15, x?B = 125 units, sB = 10 units

a) Test the null hypothesis that there is no significant difference in the mean production output between the two machines at a 5% significance level. State the null and alternative hypotheses.

b) Calculate the pooled estimate of the population variance assuming equal variances.

c) Calculate the test statistic for testing the difference in means between the two machines.

d) Determine the critical value for the test statistic and state the decision rule.

e) Make a decision regarding the null hypothesis and interpret the result.

f) Calculate a 95% confidence interval for the difference in means between the two machines.

g) Interpret the meaning of the confidence interval in the context of the problem.

h) The management of the company is interested in estimating the difference in means between the two machines with a margin of error of 2 units and a 99% confidence level. Determine the sample size required for each machine.