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Sampling and Estimation
(the average case)
Overview
• We take a simple random sample
– from a well-defined population
• The sample mean is “probably/usually” “close” to
the population mean
• By “probably/usually” we mean “in 95% of all
samples”
• By “close” we mean “within ~2 standard errors”
Populations and samples
Overview
• Defining a population
• Taking a simple random sample
• How similar is the sample to the population?
fichier-pdf.fr/2015/10/12/lecture-7-part-1/
12/10/2015
Lecture 8 Part II Confidence Intervals
Sample Size
• Assumptions
–
Population Standard Deviation Is Known
–
Population Is Normally Distributed
–
If Not Normal, use large samples
Too Big:
fichier-pdf.fr/2015/10/12/lecture-8-part-ii/
12/10/2015
Sampling distribution method
µY
– then the sampling distribution is implausible
– so you reject H0
Under the null hypothesis
Specify sampling distribution
standard error of the mean = 15
-1 SD
= 10.6lbs
1 SD
-2 SD
Under the null hypothesis
2
2 SD
-3 SD
3 SD
average
1000
weight
doctors’
fromweights
samples of 2
Relative frequency of 1000 observations of weight
mean= 150 lbs;
fichier-pdf.fr/2015/10/12/lecture-9-part-1/
12/10/2015
Oil samples placed in the test tubes before the heating test
The heater was preheated to 180 °C and samples were placed into the heater for 12 hours.
fichier-pdf.fr/2015/09/16/oil-test/
16/09/2015
Parameters of the aged cell for samples 1, sample 2 and sample 3
Sample
Operationtime [h]
Temperature
[°C]
Current
density
[mA·cm ]
Fuelgas
1
0
-
-
-
2
2 500
850
230
H2, N2
3
20 000
850
90-200
H2, N2, CH4, CO2, CO,
H2 O
Sample Preparation and the 3D reconstruction
The samples were first impregnated by low viscosity epoxy resin under vacuum
conditions so that an improved contrast could be generated between pore and solid phases.
fichier-pdf.fr/2018/08/22/fichier-pdf-sans-nom-1/
22/08/2018
essai de traction Effects of annealing on aluminum alloy
Quentin Battesti
Laboratoire de matériaux Arts et Métiers ParisTech, 8 Boulevard Louis XIV, 59046 Lille, France
Available 11 December 2016
Abstract
Uniaxial tensile tests were carried out on two different samples of aluminum.
fichier-pdf.fr/2016/04/03/essai-de-traction/
03/04/2016
KEH
GC Analysis
0314-27
# Samples 1
Sample(s) Received 03/04/2014
Enthalpy Code
Client's Sample ID
0314-27-07
1402029N-100PG
Batch/Lot/Notes
Nicotine
(mg/mL)
99.4
Summary of Method:
fichier-pdf.fr/2014/08/01/1402029n-enthalpy/
01/08/2014
doi:10.1038/nprot.2011.396
The unprecedented increase in the throughput of DNA sequencing driven by next-generation technologies now allows efficient
analysis of the complete protein-coding regions of genomes (exomes) for multiple samples in a single sequencing run.
fichier-pdf.fr/2012/03/10/nprot-2011-396/
10/03/2012
• Confidence intervals give the same
information (and more) than hypothesis tests…
Rejecting H0
• The confidence interval (CI)
• contains plausible values of µY
• One of these plausible values is right
• in 95% of all samples
• None of the values in H0 are in the CI
• So we reject H0 as implausible
Duality with hypothesis tests.
fichier-pdf.fr/2015/10/12/lecture-9-part-ii/
12/10/2015