A company has a new process for manufacturing large articial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these gems is x=6.75carats, and the sample standard deviation is s=0.33 carat. Letbe the mean weight for the distribution of all sapphires produced by the new process.(Show your work, no work shown, no credit given)

• What is the degrees of freedom in this problem?

• Use table or Technology to find t-critical value with degrees of freedom found above and with =0.05 significance level.

• Find the Margin of error (E)

• Find a 95% confidence interval for

• Interpret the condence interval in the context of the problem.