An engineer is interested in estimating the difference of two population means. For this purpose, she has collected two independent random samples (one sample from each population). Each of these random samples contains n-n2=100 observations. The first sample has the mean of 15.0 and the variance of 9.0. The second sample has the mean of 12.0 and the variance of 7.0. Based on the collected data, the engineer has obtained the following confidence interval for the difference of two population means: (2.216, 3.784). a) What is the value of a that was used for the construction of the above confidence interval? Explain. b) If the engineer constructs a confidence interval (with the same sample data) using a larger value of a than the one identified in part a, would this confidence interval narrower or wider than the interval above? Why? c) If the engineer wants to reduce the width of the confidence interval without changing the value of a, what would you recommend?