A company has a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these gems is ?¯=6.75x¯=6.75 carats, and the sample...

A company has a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these  gems is  ?¯=6.75x¯=6.75 carats, and the sample standard deviation is ?=0.33s=0.33 carat. Let ? be the mean weight for the distribution of all sapphiresproduced by the new process. (Show your work)

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 ?=0.05α=0.05  significance level.


• Find the Margin of error (E)


• Find a 95% confidence interval for ?


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