Calculation and Interpretation of the ...
The standard error (SE) of the sample mean refers to the standard deviation... Read More
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 point estimate of the population proportion p when binomial modeling is involved.
A point estimate is a specific outcome that takes a single numerical value. It has two main characteristics:
- a point estimate is a single numerical value specific to a given sample; and
- it has no sampling distribution.
Point estimates are subject to bias, where the bias is the difference between the expected value of the estimator and the true value of the population parameter involved. Each point estimate has a well-defined formula used in its calculation. Statisticians use the method of maximum likelihood or the method of moments to find good unbiased point estimates of the underlying population parameters.
Confidence Interval Estimate
We design a confidence interval estimate such that there is a range (lower confidence limit and upper confidence limit) within which analysts are confident that a population parameter lies. A probability is assigned indicating the likelihood that the designed interval contains the true value of the population parameter.
Breaking Down the Confidence Interval Estimate
There are 3 parts that collectively form an interval estimate:
- confidence level;
- a statistic; and
- a margin of error.
A confidence interval has the lower and upper limits which serve as the bounds of the interval. The level of confidence highlights the uncertainty associated with samples and sampling methods. The precision of an interval estimate depends on the sample statistic and the margin of error. The interval estimate appears as: sample statistic ± margin of error.
The Confidence Level
Suppose we compute an interval estimate with 90% confidence level, what would this mean?
We could interpret this to mean that if we were to draw multiple samples using the same sampling method and then compute different interval estimates, we would expect 90% of the constructed intervals to contain the true value of the population parameter.
The Margin of Error
The margin of error is the range of values below and above the sample statistic.
For example, suppose pollsters predict that an independent candidate will receive 25% of the votes cast in an election and the survey has a margin of error of 5% at the 95% confidence level. How do you interpret this?
It means we are 95% confident that the independent candidate will receive between 20% and 30% of the votes cast.
In conclusion, the two concepts are very useful in hypothesis testing and overall statistical analysis.
Sergio Torrico
2021-07-23
Excelente para el FRM 2
Escribo esta revisión en español para los hispanohablantes, soy de Bolivia, y utilicé
AnalystPrep para dudas y consultas sobre mi preparación para el FRM nivel 2 (lo tomé una sola vez y aprobé muy bien), siempre tuve un soporte claro, directo y rápido, el material sale rápido cuando hay cambios en el temario de GARP, y los ejercicios y exámenes son muy útiles para practicar.
diana
2021-07-17
So helpful. I have been using the videos to prepare for the CFA Level II exam. The videos signpost the reading contents, explain the concepts and provide additional context for specific concepts.
The fun light-hearted analogies are also a welcome break to some very dry content.
I usually watch the videos before going into more in-depth reading and they are a good way to avoid being overwhelmed by the sheer volume of content when you look at the readings.
Kriti Dhawan
2021-07-16
A great curriculum provider. James sir explains the concept so well that rather than memorising it, you tend to intuitively understand and absorb them.
Thank you ! Grateful I saw this at the right time for my CFA prep.
nikhil kumar
2021-06-28
Very well explained and gives a great insight about topics in a very short time. Glad to have found Professor Forjan's lectures.
Marwan
2021-06-22
Great support throughout the course by the team, did not feel neglected
Benjamin anonymous
2021-05-10
I loved using AnalystPrep for FRM.
QBank is huge, videos are great.
Would recommend to a friend
Daniel Glyn
2021-03-24
I have finished my FRM1 thanks to AnalystPrep. And now using AnalystPrep for my FRM2 preparation. Professor Forjan is brilliant. He gives such good explanations and analogies. And more than anything makes learning fun. A big thank you to Analystprep and Professor Forjan. 5 stars all the way!
michael walshe
2021-03-18
Professor James' videos are excellent for understanding the underlying theories behind financial engineering / financial analysis. The AnalystPrep videos were better than any of the others that I searched through on YouTube for providing a clear explanation of some concepts, such as Portfolio theory, CAPM, and Arbitrage Pricing theory. Watching these cleared up many of the unclarities I had in my head. Highly recommended.