Point Estimate and Confidence Interval Estimate
Point Estimate A point estimate gives statisticians a single value as the estimate of a given population parameter. For example, the sample mean X̄ is the point estimate of the population mean μ. Similarly, the sample proportion p is a…
Properties of an Estimator
A point estimator (PE) is a sample statistic used to estimate an unknown population parameter. It is a random variable and therefore varies from sample to sample. A good example of an estimator is the sample mean, \(x\), which helps…
Standard Error of the Sample Mean
The standard error (SE) of the sample mean refers to the standard deviation of the distribution of the sample means. It gives analysts an estimate of the variability they would expect if they were to draw multiple samples from the…
Central Limit Theorem
The central limit theorem asserts that when we have simple random samples, each of size n from a population with mean μ and variance σ2, the sample mean X approximately has a normal distribution with mean μ and variance σ2/n…
Comparing Probability and Non-Probability Sampling Techniques
You will recall that simple random sampling, stratified random sampling, and cluster sampling are types of probability sampling techniques. On the other hand, convenience sampling and judgemental sampling are types of non-probability sampling techniques. Probability Sampling Methods Simple Random Sampling…
Sampling Error Explained
Sampling error is the statistical error that occurs when an analyst selects a sample that is not representative of the population as a whole. In other words, it is the difference between the observed value of a sample statistic (mean,…
Probability and Non-Probability Sampling
A population is the total number of elements in a group while a sample is a portion of the population. Sample statistics—quantities such as sample mean that describe sample data—generalize the information about the population parameter. As such, we draw…
Economies and Diseconomies of Scales
Economies of Scale Economies of scale refer to the cost advantage brought about by an increase in the output of a product. Economies of scale arise due to the inverse relationship between the per-unit fixed cost and the quantity produced…
Break-even and Shut-down Points of Production
Break-even Point of Production The break-even point can be defined as the production and sales levels of a given product at which the revenue generated from the sales is perfectly equal to the production cost. At this point, the company…
Law of Diminishing Marginal Returns
The law of diminishing marginal returns states that the marginal return from an increased input, say labor, will decrease when this input is added continually to a fixed capital base. Example: Law of Diminishing Marginal Returns A good example is…
