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– In 90% of all samples, the sample mean is within 1.64 within 1.96 standard errors from the population mean (10% of samples have means that are further away).

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?

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:

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;

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.

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This article presents the development of a targeted proteomic assay to quantify 4 acute kidney injury biomarker candidates in urine samples.

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.

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.

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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:

However, …In long run (in many samples), 95% of all confidence intervals, tagged with 95% confidence, will be correct and 5% of them will be wrong.

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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.

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The levels of nicotine degradation products represented 0–4.4% of those for nicotine, but for most samples the level was 1–2%.

•  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.