Confidence Interval for a Population mean, with a known Population Variance

We have the following assumptions: Population variance σ2 is known Population is normally distributed Under these assumptions, the confidence interval estimate will be given as follows: Example Let’s take an example to compute this. We take a sample of 16 stocks from a large population with a mean return of 5.2%. We know that the […]


Confidence Interval Estimates

Along with point estimate we may also want to find a range of values within which our population parameter lies with a certain confidence level (1 – α). This is called confidence interval estimate. The α is known as the significance level and the probability (1-α) is known as the degree of confidence or confidence […]


Point Estimates

A point estimate is a single statistic value that is the “best guess” for the parameter value (such as population mean). The point estimates are calculated using formulas such as the formula to calculate the sample mean or standard deviation. These formulas are called estimators and the values calculated using these estimates are called estimates. […]


Parameter Estimation

In statistics, statistical inference refers to drawing conclusion based on the data. Statistical inferences are drawn in two broad ways, namely, hypothesis testing, and parameter estimation. In hypothesis testing, we make a hypothesis and then we determine whether the sample data supports the hypothesis or does not support it. The hypothesis could be something like […]


Standard Error of the Sample Mean

The standard error of the sample mean is calculated using the following formula. Note that the larger the sample size, the smaller will be the standard deviation. Let’s say the monthly average savings of a family in a city are $500. Based on a sample size of 50 families, the standard error will be: Standard […]


Central Limit Theorem

The Central Limit Theorem is a fundamental theorem of probability and describes the characteristics of the population of the means. According the Central Limit Theorem, for simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution of the sample means is approximately normally distributed. Here n […]


Time Series and Cross Sectional Data

In investment analysis, we observe two types of data, namely, time-series data and cross-sectional data. Time-series data refers to observations made over a period of time at regular intervals. For example, when we take daily closing prices of a stock for 1 year, it is time-series data. The time unit of observation could be anything […]


Stratified Random Sampling

Stratified random sampling is a sampling method that goes one step further than simple random sampling. It can be used in situations where the population can be separated naturally into sub-groups or strata. For example, our population of 500 stocks can be separated into sub-groups, with each group representing an industry such as Energy, Automobiles, […]


Sampling Error

Sampling error is the difference between the sample statistics (such as sample mean) and the corresponding population parameter (such as population mean). Sampling error occurs due to the random selection of the sample and can be reduced by increasing the size of the sample, or by ensuring that the sample more closely represents the population.


Simple Random Sampling and Sampling Distribution

Simple Random Sampling Simple random sampling is a type of sampling method, in which each element of the population has an equal chance of being selected in the sample. A simple random sample can be selected as follows: List all the items in the population say from 1 to N, where N is the total […]