When drawing conclusions about a population from randomly chosen samples (a process called statistical inference), you can use two methods: confidence intervals and hypothesis testing. A confidence interval is a range of values that's expected to contain the
value of a population parameter with a specified level of confidence (such as 90 percent, 95 percent, 99 percent, and so on). For example, you can construct a confidence interval for the population mean by following these steps: Estimate the value of the population mean by calculating the mean of a randomly chosen sample (known as the sample mean). Calculate the lower limit of the confidence interval by subtracting a margin of error from the sample
mean. Calculate the upper limit of the confidence interval by adding the same margin of error to the sample mean. The margin of error depends on the size of the sample used to construct the confidence interval, whether the population standard deviation is known, and the level of confidence chosen. The resulting interval is known as a confidence interval. A confidence interval is constructed with a specified level of probability. For example, suppose you draw
a sample of stocks from a portfolio, and you construct a 95 percent confidence interval for the mean return of the stocks in the entire portfolio: (lower limit, upper limit) = (0.02, 0.08) The returns on the entire portfolio are the population of interest. The mean return in each sample drawn is an estimate of the population mean. The sample mean will be slightly different each time a new sample is drawn, as will the confidence interval. If this process is repeated 100 times, 95 of the resulting confidence intervals will contain the true population mean. Hypothesis testingHypothesis testing is a procedure for using sample data to draw conclusions about the characteristics of the underlying population. The procedure begins with a statement, known as the null hypothesis. The null hypothesis is assumed to be true unless strong evidence against it is found. An alternative hypothesis — the result accepted if the null hypothesis is rejected — is also stated. You construct a test statistic, and you compare it with a critical value (or values) to determine whether the null hypothesis should be rejected. The specific test statistic and critical value(s) depend on which population parameter is being tested, the size of the sample being used, and other factors. If the test statistic is too extreme (for example, it's too large compared with the critical value[s]) the null hypothesis is rejected in favor of the alternative hypothesis; otherwise, the null hypothesis is not rejected. If the null hypothesis isn't rejected, this doesn't necessarily mean that it's true; it simply means that there is not enough evidence to justify rejecting it. Hypothesis testing is a general procedure and can be used to draw conclusions about many features of a population, such as its mean, variance, standard deviation, and so on. About This ArticleAbout the book author:Alan Anderson, PhD is a teacher of finance, economics, statistics, and math at Fordham and Fairfield universities as well as at Manhattanville and Purchase colleges. Outside of the academic environment he has many years of experience working as an economist, risk manager, and fixed income analyst. Alan received his PhD in economics from Fordham University, and an M.S. in financial engineering from Polytechnic University. This article can be found in the category:
We often have questions concerning large populations. Gathering information from the entire population is not always possible due to barriers such as time, accessibility, or cost. Instead of gathering information from the whole population, we often gather information from a smaller subset of the population, known as a sample. Values concerning a sample are referred to as sample statistics while values concerning a population are referred to as population parameters. Population The entire set of possible cases Sample A subset of the population from which data are collected Statistic A measure concerning a sample (e.g., sample mean) Parameter A measure concerning a population (e.g., population mean) The process of using sample statistics to make conclusions about population parameters is known as inferential statistics. In other words, data from a sample are used to make an inference about a population. SamplePopulation SamplingINFERENCEInferential Statistics Statistical procedures that use data from an observed sample to make a conclusion about a population What is the conclusion drawn about population based on information in a sample?statistical inference. The process of drawing a sample from a population and then carrying out statistical analysis on the sample in order to make conclusions about the entire population is called statistical inference.
Which sampling method allows to draw valid conclusions about population?Stratified sampling involves dividing the population into subpopulations that may differ in important ways. It allows you draw more precise conclusions by ensuring that every subgroup is properly represented in the sample.
What is the population that the researchers can draw conclusions about?A “population of interest” is defined as the population/group from which a researcher tries to draw conclusions. It is a subset of the general population that the surveyor wants to know more about. Many research studies require specific groups of interest to make decisions based on their findings.
What is the name of the population from which a sample is drawn?Sampling frame: a list of the population from which a sample is drawn. Sampling with replacement: a sample in which one can replace subjects into the sampling frame after each draw.
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