Twenty years ago, entering male high school students of Central High could do an average of 24 pushups in 60 seconds. To see whether this remains true today, a random sample of 36 freshmen was chosen. If their average was 22.5 with a sample standard deviation of 3.1, can we conclude that the mean is no longer equal to 24? Use the 5 percent level of significance.

ST 701 Week 10 Notes MaLyn Lawhorn October 19, 2017 Joint Distributions In the real world, we normally care about experiments that involve more than one random variable. Speciﬁcally, we are interested in the relationship among the n random variables. We are going to focus on the n = 2 (bivariate case) for now. The general n case is the same, just more tedious. CDF for Bivariate Experiments The notation for a cdf of a bivariate experiment is F XY(x;y) = P(X ▯ x;Y ▯ y): Visually, we can think of this as area on a graph. Y y X x PDFs and PMFs