{"id":1918,"date":"2019-05-17T12:00:00","date_gmt":"2019-05-17T10:00:00","guid":{"rendered":"https:\/\/kindsonthegenius.com\/blog\/statistics-questions-and-answers\/"},"modified":"2026-07-05T03:23:20","modified_gmt":"2026-07-05T01:23:20","slug":"statistics-questions-and-answers","status":"publish","type":"post","link":"https:\/\/kindsonthegenius.com\/blog\/statistics-questions-and-answers\/","title":{"rendered":"Statistics Questions and Answers"},"content":{"rendered":"

This is a list of some statistics questions and answers. The answers and brief and clear.<\/p>\n

 <\/p>\n

What is Biased and Unbiased Statistic?<\/strong><\/h4>\n

We actually talk about unbiased estimate. A sample statistic is considered and unbiased estimate of\u00a0 the population parameter if the mean of the sampling distribution of that statistic equals the parameter being estimated.<\/p>\n

For instance, if we draw a sample from population, then the mean of this sample (sample mean) would be an unbiased estimate if it is equal to the mean of the population from which the sample was taken.<\/p>\n

 <\/p>\n

What is Consistent Estimate<\/strong><\/h4>\n

A statistic on a sample size of n is said to be consistent if the if as the n increases,the estimated converges to the actual value of the parameter.<\/p>\n

 <\/p>\n

What is Efficiency in Statistics?<\/strong><\/h4>\n

Efficiency is a measure of the quality of an estimate. Generally, a more efficient efficient estimate would require fewer sample size(observations) than a less efficient estimate for a particular performance.<\/p>\n

For example, let’s take two unbiased estimators T1<\/sub> and T2<\/sub>.<\/p>\n

T1<\/sub> is considered more efficient than T2<\/sub>, if for n number of observations<\/p>\n

\u03c32<\/sup>T1<\/sub> <\u00a0\u03c32<\/sup>T2<\/sub><\/p>\n

for any parameter\u00a0\u03b8<\/p>\n

 <\/p>\n

What is Sufficient Statistic?<\/h4>\n

Sufficient statistics is a statistic that contains the summary of all the information about the parameter being estimated.<\/p>\n

For example, we want to estimate the population parameter\u00a0\u00b5, take a sample of size n = 4. The realization of this sample is (2, 3,4,7). This means that we would have a sample mean of (2+3+4+7)\/4 = 4. So four is our estimate. Also, if the sample was (1, 4, 5,6), it would also give us a sample mean of 4.<\/p>\n

Therefore the sample mean could cover a combination of observations that is well covered by the parameter being estimated. In this case, we say that the estimate is sufficient.<\/p>\n

 <\/p>\n

Cramer-Rao Inequality<\/strong><\/h4>\n

The Cramer-Rao inequality gives a measure of the lower bound for the variance of an unbiased estimator of a given parameter. We can used it to determine that an estimator is a minimum variance unbiased estimator(MVUE).<\/p>\n

 <\/p>\n

Differentiate Between Point Estimate and Interval Estimate<\/strong><\/h4>\n

A point estimate provide an estimated value of a single number while an interval estimate provides a range of values within which the estimated parameter is likely to lie.<\/p>\n

 <\/p>\n

What is Confidence Interval?<\/strong><\/h4>\n

This is an interval or range of values provided by the estimation process. It provides us with the possibility or confidence that the value of the unknown parameter lies within this range.<\/p>\n

The figure below shows the difference between point estimate, interval estimate and confidence interval<\/p>\n

\"Point
Explaining Point estimate, interval estimate and confidence interval<\/figcaption><\/figure>\n

 <\/p>\n

What is difference between Parametric and Non-parametric Test?<\/strong><\/h4>\n

Parametric tests<\/a> are statistical tests that makes assumption about the distribution of the data. It assumes that the data follows a normal distribution. Examples of parametric tests includes:<\/p>\n