Estimation & Confidence of interval

Nov 30, 2020

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Lot more to correct and lot more to add

• Defination wise, Estimation is a process of making a references about population based on information obtained from a sampele.

• we can understand estimation from a simple project assignment example that is, Suppose i have assigned a work to you and asking you in how many time this project will be completed.then you should tell me like in 1-2 days i will complete this project or in 4-5 months i will complete.indirectly you are giving me a range or a time of interval so you are estimating a range with a confidence.

Confidence of Interval

Confidence Interval refers to the probability that a population parameter will fall between two set of values or interval.

• Confidence Interval also indicates that the range that’s likely to contain the true population parameter, so the CI focuses on the population.

• the interval estimate of a confidence interval is defined by sample statistic ± margin of error.

• The probability part of a confidence of interval is called a confidence level (α).Here α lies between 0 and 1.

  example : If we are 95% confident then α is 5%.

• In a confidence interval, the range of values above and below the sample statistic is called the margin of error.

• let's take a another example, in a sales company before selling a product we have to estimate the number of product according to the past sales of the similar product. If you didn't estimate a number or interval, company will be in loss. How? let say market capacity od that perticular product is 100 and the company built only 80 even company can build 100 as well but company didn't anayse the past data and didn't set an estimate so company will be in loss.

• Estimation is used in most of the area's like sales, investment, marketing, banking etc

• correct estimation is very much important.

Some important points:

• The confidence level is not affected by margin of error.
• The confidence interval is a type of interval estimate not a type of point estimate.
• A sample mean is a example of point estimate not population mean.

Point estimation

• A point estimation of a population is a single value of a statistics.
• It is not good to make a single number estimation in real world.

Interval Estimation

• Gives a range depend upon the confidence.
• In which estimation lie in a range between two values and can be anything between those two values.

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1. In case of high confidence, chances or failure will be high so keep the margin as low as possible so that you can cover up the loss.
2. In case of low confidence, chances of failure will be low but other factor will also effect.

Confidence interval = X ± (Zα/2 * σ/√n) Confidence interval = 1 - α

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1 - α = X ± (Zα/2 * σ/√n)

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X = mean
Zα/2 = the confidence coefficient
σ = standard deviation
n = sample size
here (1-α) is confidence interval and α is confidence level which will help us to find out the z-value from z-table.

let say our eastimtion lie between 300 to 350 that means, with x% of confidence, we have to build at least 300 products.

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for sample size n > 30
Confidence interval = X ± (z * σ/√n) 
where z critical value is derived from the z score table based on the confidence level.
for sample size n < 30
Confidence interval = X ± (t * s/√n)
where t critical value is derived from the t score table based on the confidence level.

Hypothesis & hypothesis testing >