I need help with this as I have to round the decimal answers to at least 3 places, unless otherwise, but I wanted to see If I am doing it correctly as I am using the R coding program to solve the question.

Who studies more, college freshmen or sophomores? The mean number of hours, l'x , that freshmen study per week will be compared to the mean number of hours, ,4, that sophomores study per week. The true values of \"x and by are unknown. It is recognized that the true standard deviations are ax = 6.3 hours for freshmen and a, 5.8 hours for sophomores. We take a random sample ofm = 27 freshmen and n: 38 sophomores The mean numbers of hours studying were were ;= 39.6 for the freshmen and ;= 35.4 for the sophomores Assuming all measurements were independent from an: another and assuming that hours studied are normally distributed we would like tn estimate 14x by. a) What is the standard deviation of the distribution of ;? :I b) What is the standard deviation of the distribution of} - y ? [j c) Create a 98% condence interval for \"X by 7 (l: , :D d) What is the length of the condence interval in part c) ? E e) If we let n stay at 38 but vary m, what is the smallest m for which the length of the 98% condence interval would be 5.0 or less? [:] 7. Do forest fires near streams hurt fishing in those streams in future years. There are arguments for and against thesis thesis. The mean number of trout, Ux caught by an angler in a day of fishing in the Yellowstone River before the 1988 super fires will be compared to the mean number of trout, My caught by an angler in the same river in 1993. The true values of ux and My are unknown. It is recognized that the true standard deviations are Ox = 1.9 for the before 1988 measurements and oy = 2.3 for the 1993 measurements. We take a random sample of m = 167 angler catches before 1988 and a random sample of n=125 angler catches in 1993. The mean angler catches were were x = 5.2 for the before 1988 measurements and y = 6.8 for the 1993 measurements. Assuming independence between the years and assuming angler catch amounts are normally distributed we would like to estimate Ux - My. a. What is the standard deviation of the distribution of x ? b. What is the standard deviation of the distribution of x - y? c. Create a 94% confidence interval for Ux - My? d. What is the length of the confidence interval in part c? e. If we let n stay 125 but vary m, what is the smallest m for which the length of the 96% confidence interval would be 0.88 or less? > #7 trout catch before and after forest fires >m ybar sigmax sigmay zstar zstar [1] 1.880794 > # 94 % confidence interval > c(xbar - ybar - zstar*sediff, xbar - ybar + zstar*sediff) #c [1] -2. 075572 -1. 124428 >#d Length of conf int: > 2*zstar*sediff #d length of conf int. [1] 0.9511444 >#e) Let m vary. Smallest m for which length of confidence interval is . 88 or less. fl ll LL [1] 290.9014 ceiling(11) # smallest m [1] 291