Download presentation

Presentation is loading. Please wait.

Published byNelson Milam Modified over 2 years ago

1
1 Confidence intervals

2
2 Point and interval estimators There are two kind of estimators: Point Interval Point estimator: single statistics used for rstiamte a paramether of the population. Sample mean is a point estimator for the mean of the population , sample variance is a point estimator for the variance of the population 2, ecc.

3
3 Point and interval estimators Interval estimator: interval of values that has a certain probability or confidence to contain the true value of the paramenter of the population. The level of confidence is usually (1- )% where is the probability that the value stays in the tails of the distribution, outside the confidence interval.

4
4 Intervallo di confidenza per la media noto il valore dello scarto quadratico medio La statistica per costruire intervalli di confidenza per la media è Ovvero una distribuzione Normale standardizzata, “indipendentemente” dalla distribuzione originale della variabile X (campioni sufficientemente grandi). Da tale distribuzione scaturiscono gli estremi dell’intervallo di confidenza per la media.

5
5 Confidence interval for the mean known σ of the poplulation When the population is normally distributed, the distribution of the mean is also normal When population variable X is normally distributed and is known, a 100(1 − α)% confidence interval for μ is given by

6
6 Confidence interval Normal curve for Z with a level of confidence of 95% Normal curve for Z with a level of confidence of 99%

7
Example Bolts produced from a firm have an unknown mean diameter, its variance is 0.01. We keep a sample of n=1000 bolts and we observe a mean diameter of 1.2 cm. Find the confidence interval at 99% with a fixed level of confidence of 99%. 1-α=0.99→ α=0.01 → α/2=0.005 →1-α/2=0.995 From table of Normal distribution Z(0.995) =2.576 So the interval is

8
8 Confidence interval for the mean unknown σ of the poplulation Given that σ is not know we need to use its estiamator s. If we consider the ratio then the random variable t has the Student’s t distribution with n − 1 degrees of freedom. A 100(1−α )% confidence interval for μ is given by where t α/2 is the upper α/2 point of the Student’s t distribution with n − 1 degrees of freedom.

9
9 If n is very large the t distribution is very close to a Normal distribution. Confidence interval for the mean unknown σ of the poplulation

10
10 The table of the Student’s t distribution give the probability (area) on the right of the indicated value. Confidence interval for the mean unknown σ of the poplulation

Similar presentations

Presentation is loading. Please wait....

OK

Statistical Intervals for a Single Sample

Statistical Intervals for a Single Sample

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

History of computers for kids ppt on batteries Ppt on history of badminton sport Ppt on spiritual tourism in india Convert doc to ppt online Ppt on history of olympics sports Ppt on role of electronic media in communication Certificate templates free download ppt on pollution Ppt on question tags test Ppt on computer malware spyware Download ppt on pedal powered washing machine