The following table gives the summary.r statistics for two simple random samples of the heights [in inches) of men and women at a university. Find a 98% condence interval for the difference in average heights of men and women at the university. Assume the population standard deviations for the heights of men and women (01 and 0'2} are unknown and are NOT EQUAL (01 75 a2). lHeights for men (Group 1) Heights for women [Group 2) Sample mean f3 69 Sample standard deviation '24 1.8 Sample size '65 51 Let p1 the true average height for (all) men and p2 the true average height for (all) women at this university. Answer all parts below: (a) What is the best estimate for the difference between the true average heights of men and women 31.1 #2? Nu mber (inches) (b) What is the best distribution that you would use in order to construct a condence interval for the difference in average heights of men and women at this university? 0 Use tdistribution with a number of degrees of freedom (if = 114 0 Use z-distribution. Use tdistribution with a number of degrees of freedom df = 50 (c) A 98% condence interval for the difference ,ul .152 between the average heights of men and women at this university.r is between Number and Number (inches) Round the lower and upper bounds to 3 decimal places