1. An engineering team is making updates to an existing product with the goal of improving the functionality of the product. The team measures a sample of 12 existing products and a sample of 14 updated products. Based on their sample measurements, the existing product has a sample mean of 22.7 and sample standard deviation of 2.86 and the updated product has a sample mean of 24.3 and sample standard deviation of 2.42. Assume the population variances are equal. a. Construct a 95% confidence interval for the difference between the means of the existing and updated product and interpret. b. If the functionality of the product is improved by having measurements greater than the existing product, with a significance level of 0.05, can the team make the claim the functionality has improved? Why or why not? Explain your reasoning. c. Say there is an assumed known population variance of 12. Construct an updated 95% confidence interval for the difference between the means of the existing and updated product and interpret. How does this compare to the confidence interval from part a? Would this change your answer in part b? If so, how? Explain your reasoning. d. It was discovered there had been an error in the measurements of the sample of the updated product due to an operator using an uncalibrated machine. After re-measuring the 14 samples of the updated product, the sample mean is 25.4 and sample standard deviation is 1.72 and they can no longer assume the population variances are equal. Revise the 95% confidence interval for the difference between the means of the existing product and the updated product (from part a) and interpret. Does this change your answer in part b? If so, how? Explain your reasoning