Question

In: Statistics and Probability

1- Describe in detail who first introduced the Confidence Intervals & Estimation process in Statistics, his...

1- Describe in detail who first introduced the Confidence Intervals & Estimation process in Statistics, his background and contribution to the field of statistics?

2- Describe in detail a Confidence Interval Estimate is a type of interval estimate that is computed from an observed data?

Solutions

Expert Solution

1)

Confidence intervals were introduced to statistics by Jerzy Neyman in a paper published in 1937

He was a Polish mathematician and statistician who spent the first part of his professional career at various institutions in Warsaw, Poland and then at University College London, and the second part at the University of California, Berkeley. Neyman first introduced the modern concept of a confidence interval into statistical hypothesis testingand co-revised Ronald Fisher's null hypothesis testing (in collaboration with Egon Pearson).

He published many books dealing with experiments and statistics, and devised the way which the FDA tests medicines today.

Neyman proposed and studied randomized experiments in 1923. Furthermore, his paper "On the Two Different Aspects of the Representative Method: The Method of Stratified Sampling and the Method of Purposive Selection", given at the Royal Statistical Society on 19 June 1934, was the groundbreaking event leading to modern scientific sampling. He introduced the confidence interval in his paper in 1937.[6] Another noted contribution is the Neyman–Pearson lemma, the basis of hypothesis testing.

2)

In statistics, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown population parameter. The interval has an associated confidence level that, loosely speaking, quantifies the level of confidence that the parameter lies in the interval. More strictly speaking, the confidence level represents the frequency (i.e. the proportion) of possible confidence intervals that contain the true value of the unknown population parameter. In other words, if confidence intervals are constructed using a given confidence level from an infinite number of independent sample statistics, the proportion of those intervals that contain the true value of the parameter will be equal to the confidence level.

for example t-test

Xbar and s , n are statistics based on sample


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