1) One manager, Chelsea, thinks that the main problem is a new axle manufacturing process that is incorrectly calibrated. The drive shaft needs to be 30 inches with little variation, and Edgar wonders whether the new process deviates from this length. The engineers recently sampled 65 drive shafts, finding an average length of 29.97 inches, and they know that the standard deviation of the process historically is .1 inches.
a) Please state the null and alternative hypotheses to be tested here, along with what test statistic you will use and why. Calculate the p-value of this test statistic and state whether Chelsea's suspicion is correct with 95% confidence. (Please show the Excel formula you use to calculate the p-value, or the code from whatever other tool you use)
b) Using your p-value from part a, can we support Chelsea's suspicion with 99% confidence?