Problem 11.6 , 13.6 and 14.18 with steps please

Problem 11.6 16 professional marathon runners participated in a 3-month training program which included one hour of swimming three times a week. The best personal time (BPT) in minutes for a 5 km run of these athletes was recorded, before and after the training program. The data is summarized in the following table: BPT Before | BPT After Difference (x) (y) (d = x- y) Mean 30.8 29.1 1.7 Standard Deviation 5.2 4.1 1.6 Using this data, can we say that integrating swimming into the training practice of professional runners improves their BPT? Use a test of hypotheses of level a = 0.005. Assume that variables X, Y and D are normally distributed, and the variables X and Y have the same variances. Problem 13.6 We would like to describe the relationship between the mean adult female body mass (in kg) of grizzly bears (y) and the percentage of meat in the diet (x). Below are the data for n = 12 different regions. y y 5 120 42 169 6 122 42 171 7 117 60 201 11 129 76 210 12 132 77 225 26 139 79 220 (a) Calculate the mean and standard deviation for the mean adult female body mass and for the percentage of meat in the diet. (b) Draw a scatter plot of the mean adult female body mass against the percentage of meat in the diet. (c) Calculate the sample covariance and the sample correlation between the percentage of meat in the diet and the mean adult female body mass. Problem 14.18 A public official believes that the mean household water use is 1,315 liters per day. A study of water usage involved a random sample of twenty five households. The data are given below. Assume that the household water use is normally distributed. 1316 1341 1303 1322 1335 1306 1320 1307 1352 1344 1329 1342 1301 1317 1311 1328 1290 1322 1310 1348 1324 1322 1339 1334 1369 (a) Using these data, is there enough evidence to conclude that the mean household water use is not 1,315 liters per day? Use a = 0.05. (b) Construct a 90% confidence interval for the mean household water use per day