Category: Inferential Statistics

A further point concerns the correct interpretation of the confidence level. Consider the 95% confidence interval we calculated in Example 9.8. We cannot say that the confidence interval (34.0893, 84.5107) contains the unknown expected value with probability 95%. What we can say is that if we repeat the sampling procedure many times, and we compute a confidence interval for each…

Consider the queueing system in Fig. 9.2. Customers arrive according to a random process. If there is a free server, service is started immediately; otherwise, the customer joins the queue and waits. Service time is random as well, and whenever a server completes a service, the first customer in the queue (if any) starts her service.…

The sample mean is a point estimator for the expected value, in the sense that it results in an estimate that is a single number. Since this estimator it is subject to some variance, it would be nice to have some measure of how much we can trust that single number. In other words, we would like to…

The typical estimator of variance is sample variance: This formula can be understood as a sample counterpart of the definition of variance: It is basically an average squared deviation with respect to sample mean. When doing calculations by hand, the following rearrangement can be useful: The sample standard deviation is just S, the square root of sample variance. We…

The sample mean is a well-known concept from descriptive statistics: If data come from a legitimate random sample, sample mean is a statistic. A natural use of sample mean is to estimate the expected value of the underlying random variable, that is unknown in practice. It is important to understand what we are doing: We are using a…

Inferential statistics relies on random samples. There are many ways to take a sample: The last point should be stressed: Quite often we assume that observed data have been generated by a process that we represent as a statistical model. If we want to use tools from probability and statistics, this is a necessary step. However, we…

We have modeled uncertainty using the tools of probability theory. Problems in probability theory may require a fair level of mathematical sophistication, and often students are led to believe that the involved calculations are the real difficulty. However, this is not the correct view; the real issue is that whatever we do in probability theory…