A large manufacturing company replaces its production machine every five years. The manufacturing company claims that their new production machine will increase their productions. To justify this, the manufacturer selects 15 days’ productions and compares it to their previous record. They find that the mean and standard deviation of the differences (before–after) is 245 products with a standard deviation of 14 products.

a) What is the standard error of the mean difference?

b) How many degrees of freedom does the t-statistic have?

c) What is the 90% confidence interval for the mean difference?

d) What do you conclude at a = 0.1?