Dr. Raju Chaudhari 
Confidence Interval for Variance with Examples In this tutorial we will discuss some numerical examples to understand how to construct a confidence interval for population variance or population standard deviation. Example 1 The mean replacement time for a random sample of 12 microwaves is 8.6 years with a standard deviation of 3.6 years. Construct a …
Introduction Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. One such a parameter that can be estimated is a population mean. In this article we will discuss step by step procedure to construct a confidence interval for population mean when the population …
This tutorial covers examples on confidence interval for the population mean when the population standard deviation is unknown. Example 1 A new brand of laptop battery is produced by a company. The company claims that the battery will last for an extended period of time before a recharge is necessary. A sample of 40 batteries …
Introduction Confidence interval can be used to estimate the population parameter with the help of an interval with some degree of confidence. One such a parameter that can be estimated is a population mean. In this article we will discuss about the derivation and step by step procedure to construct a confidence interval for population …
Confidence Interval for Mean Use this calculator to compute the confidence interval for population mean when the population standard deviation is known. Confidence Interval Calculator for mean Sample Size ($n$) Sample Mean ($\overline{x}$) Population Standard Deviation ($\sigma$) Confidence Level ($1-\alpha$) Select90%95%98%99% Calculate Results Standard Error of Mean: Z Critical Value : ($Z$) Margin of Error: …
Bonferroni’s Inequality For $n$ events $A_1,A_2,\cdots, A_n$ $$ \begin{equation}\label{bof} P\big(\cap_{i=1}^n A_i\big)\geq \sum_{i=1}^n P(A_i) -(n-1). \end{equation} $$ Proof For $n =2$, $$ \begin{equation*} P(A_1\cup A_2)= P(A_1)+P(A_2) -P(A_1\cap A_2) \end{equation*} $$ But $P(A_1\cup A_2)\leq 1$. Using this in above equation, we have $$ \begin{eqnarray*} & &P(A_1\cup A_2)= P(A_1)+P(A_2) -P(A_1\cap A_2)\leq 1 \\ \implies & & P(A_1\cap A_2) …
