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Topic: Sample mean

	The Sample Mean and the Law of Large Numbers
		The sample mean is a real-valued function of the random sample and thus is a statistic.
		From Exercise 3, the variance of the sample mean is an increasing function of the distribution variance and a decreasing function of the sample size.
		Note that the mean of the sample mean stays the same, but the standard deviation of the sample mean decreases (as we now know, in inverse proportion to the square root of the sample size).
	www.ds.unifi.it /VL/VL_EN/sample/sample2.html (820 words)

	Mean - Wikipedia, the free encyclopedia
		Sample mean is often used as an estimator of the central tendency such as the population mean.
		The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not the same as the middle value (median), or most likely (mode).
		The geometric mean is an average that is useful for sets of numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean).
	en.wikipedia.org /wiki/Mean (906 words)

	Sample Size Effect On The Sample Mean Applet
		How it works: Students may generate samples of different sizes and see the means of the samples plotted vs. sample size on the plot abpve.
		Students can see the center of the distribution does not depend on sample size, but the variability of the mean decreases as sample size increases.
		The mean and standard deviation of the normal distribution which the samples come from can be changed in the parameter statement.
	www.stat.sc.edu /~west/applets/samplemean.html (126 words)

	CHAPTER 9
		To answer this, we need to know the sampling distribution for possible differences between the means of two different samples taken from the same population.
		A sample mean is a random variable and varies from sample to sample.
		As in part (a), the symbol t is used because the sample standard deviation (rather than the population standard deviation) is used.
	www-rohan.sdsu.edu /~hnoble/stat119hw6solns.htm (1406 words)

	PSY 138: Social Science Reasoning Using Statistics (Site not responding. Last check: 2007-10-22)
		The dots in the center of the intervals are the point estimates of the intervals (that is, they're the sample means).
		for the population and have a sample mean to compare to the population.
		You also have a sample mean to compare to the population and a sample standard deviation (s) to use to calculate estimated standard error.
	lilt.ilstu.edu /cliu/teaching/psy138/24_Lab.htm (2006 words)

	UBC - BIOLOGY 300
		We can convert values (means) from this distribution of sample means to generate the standard normal distribution, Z. We subtract the parametric mean of the population from each sample mean, and divide the result by the standard error of the mean.
		Sample statistics such as the mean or standard deviation are estimates of population parameters.
		The 95% confidence intervals for the mean are displayed on both the quantile and outlier boxplots as a diamond shape, with the mean being the midpoint of the diamond.
	www.zoology.ubc.ca /courses/bio300c/lab/jmp4t1sample.htm (1325 words)

	MATH250 - Tutorial on Sample Mean
		If the sample size is very small relative to the population size, it really does not matter whether you use sampling with or without replacement, but if the sample size is of the same order of magnitude as the population size, it does matter which of the two methods is used.
		Sampling has a variety of uses, but we are only concerned with sampling as a tool to estimate the mean of a random variable X. The population on which X is defined is often called the PARENT POPULATION.
		Suppose the mean number of miles driven by the owner of a Nissan in one year is 14,000, with a standard deviation of 1,000 miles.
	www.math.ohiou.edu /~just/FALL250/sampl4.htm (1399 words)

	The Sample Mean and the Law of Large Numbers
		In the simulation of the sample mean experiment, the density function of the basic distribution is shown in blue in the left graph, and the mean and standard deviation of this distribution are recorded in the first table.
		The density function of the sample mean is shown in blue in the right graph, and the mean and variance of this random variable are recorded in the third table.
		From Exercise 2, the variance of the sample mean is an increasing function of the distribution variance and a decreasing function of the sample size.
	www.fmi.uni-sofia.bg /vesta/Virtual_Labs/sample/sample2.html (877 words)

	Examining Sampling Distributions (Site not responding. Last check: 2007-10-22)
		This example looks at the sampling distribution of the sample mean and the sample median for samples of different sizes.
		The simulation below takes a random sample of size n from the population of 72 guinea pigs and calculates the sample mean.
		It does this repeatedly nsim times, thus obtaining a random sample from the sampling distribution of the sample mean.
	www.stat.umn.edu /~drak0020/classes/3011/examples/samplingd.html (242 words)

	Moments (Site not responding. Last check: 2007-10-22)
		Likewise, the grouped sample variance (the square of the standard deviation) is proportional to the moment of inertia (a measure of the rotational inertia of an object).
		Karl Pearson was the first to use the term moment as a descriptor for the sample mean and standard deviation based on the analogy between mechanics and statistics.
		The sample median is less affected by skewness than the sample mean, i.e., the position of the upper or lower values has little affect on the median (which is the middle value of a ranked dataset).
	www.stat.wvu.edu /SRS/Modules/Moments/moments.html (929 words)

	Sample_Final
		In a test of hypothesis, the null hypothesis is that the population mean is equal to 60 and the alternative hypothesis is that the population mean is not equal to 60.
		A sample of size 36 from this population produced a sample mean of 63.
		In a test of hypothesis, the null hypothesis is that the population mean is equal to 90 and the alternative hypothesis is that the population mean is not equal to 90.
	www.marin.cc.ca.us /~npsomas/Stats/Final/Sample_Final.htm (2479 words)

	Statistics Glossary - Basic Definitions
		For example, the population mean is a parameter that is often used to indicate the average value of a quantity.
		The sampling distribution is the probability distribution or probability density function of the statistic.
		For example, the sample mean is an estimator of the population mean.
	www.cas.lancs.ac.uk /glossary_v1.1/basicdef.html (1069 words)

	[No title]
		Sample Variance The sample variance, S2, is a measure of how widely dispersed the sample is. The sample variance is an estimator of the population variance, (2.
		A random sample of 1200 employees yields a sample mean of $361 and a sample deviation of $110.
		The distribution used is the chi-square distribution with n-1 degrees of freedom (where n = sample size), and the test statistic is given by: EMBED Equation.2 , where s2 is the sample variance and the denominator is the value of the variance stated in the null hypothesis.
	dollar.biz.uiowa.edu /~street/6n216f03/etc/week5_handouts.doc (2905 words)

	1.3.5.2. Confidence Limits for the Mean
		Confidence limits for the mean (Snedecor and Cochran, 1989) are an interval estimate for the mean.
		Interval estimates are often desirable because the estimate of the mean varies from sample to sample.
		Instead of a single estimate for the mean, a confidence interval generates a lower and upper limit for the mean.
	www.itl.nist.gov /div898/handbook/eda/section3/eda352.htm (894 words)

	The Behavior of the Sample Mean
		The behavior (distribution) of the mean of samples of 100 individual values is nearly indistinguishable from the normal distribution to the resolution of the display.
		The Sample Mean As an Estimate of The Population Mean
		If the population mean is unknown, but the sample mean is 1980 kcal, we would say we were 95% confident that the population mean was in the range (1900[=1980-80], 2060[=1980+80]) kcal.
	www.tufts.edu /~gdallal/meandist.htm (2507 words)

	The Ubiquitous Sample Mean!
		To decrease the uncertainty by a factor of 2, the sample size must be increased by a factor of 4; to cut the uncertainty by a factor of 10, a sample 100 times larger is required.
		Because the sample size is large, the distribution of individual incomes is irrelevant to constructing confidence intervals for the population mean.
		The sample mean describes both the population mean and an individual value drawn from the population.
	www.tufts.edu /~gdallal/means.htm (1275 words)

	MMU - Research Design, Biol Sci:Analysis: Power examples (Site not responding. Last check: 2007-10-22)
		Determining minimum sample size required to achieve a specified precision in a sample mean.
		Sample statistics such as the standard error and confidence intervals can be used to measure the precision of the estimate.
		to estimate the population mean with a precision of ± 10% the required precision would be 1.85 minutes (based on the sample mean).
	obelia.jde.aca.mmu.ac.uk /new_rd/contents/power2.htm (989 words)

	The Parametric Bootstrap and Exponential Distributions (Site not responding. Last check: 2007-10-22)
		This Java applet plots histograms for the sample mean, using the parametric bootstrap and i.i.d.
		We find 1000 sample means (where the sample size is n) in order to approximate the distribution of the sample mean.
		The sample mean distribution begins with with samples of size n=1 and ends with n=45.
	www.ms.uky.edu /~lancastr/java/parabootexp.html (367 words)

	SurfStat.australia (Site not responding. Last check: 2007-10-22)
		The shape of the histogram depends on the size n of the sample, and approximates to the sampling distribution.
		is the random variable from which each sample mean is an observation.
		Hence, plausible values for µ are 164-166 cms, or with 95% confidence the true study population mean height of women aged 25-29 years lies between 164 and 166 cms.
	www.anu.edu.au /nceph/surfstat/surfstat-home/4-1-4.html (540 words)

	Sample Mean (from Internet Glossary of Statistical Terms)
		The mean of a random sample is an unbiased estimate of the mean of the population from which it was drawn.
		Most statisticians use (n) to represent the number of items in a sample, whereas they use the symbol (N) to represent the number of items in a population.
		For this sample from this population n=4, N=9.
	www.animatedsoftware.com /statglos/sgxbar.htm (137 words)

	Power examples
		Sample means estimate population means and sample statistics such as the standard error and confidence intervals can be used to measure the precision of the estimate.
		The process is iterative, in that an estimate of the population standard deviation is needed.
		The sample size of 5 is in close agreement with the results generated by Power Plant.
	www.iph.ufrgs.br /corpodocente/marques/cd/rd/power2.htm (940 words)

	Sociology 712 (Site not responding. Last check: 2007-10-22)
		We calculate a t-score for the sample mean, and consult the t-table to determine whether the sample data supports the research or null hypothesis.
		We take a random sample of 75 countries and consult the archives of Amnesty International, The International Court of Justice, the United Nations and the World Bank, and determine that the sample mean is 3,292.8 with a standard deviation of 4,814.5.
		The t-test for one sample mean allows us to estimate the population mean on some variable, and to test a hypothesis about it.
	academic.brooklyn.cuny.edu /soc/courses/712/chap12.html (1552 words)

	Definition: Sample mean (Site not responding. Last check: 2007-10-22)
		The sample mean (often represented by the symbol XBAR) is the average of all the items in a sample.
		The sample mean is a lot easier to compute because the size of the sample is usually quite manageable.
		If the sample is chosen carefully, the sample mean is a good estimate of the population mean.
	www.cmh.edu /stats/definitions/mean.htm (211 words)

	Math 225 Section 5.3 (Site not responding. Last check: 2007-10-22)
		For most problems, the central limit theorem allows us to conclude that the shape of the distribution is approximately normal, and we can use methods from chapter 4 to answer questions about the probability of the sample mean falling in various intervals.
		This reflects the fact that the mean from a sample is more likely to be close to the population mean than a randomly chosen individual.
		In a recent year, the birthweights of infants born in Boston had a mean weight of 112.0 ounces with a standard deviation of 20.6 ounces.
	www.mathcs.duq.edu /larget/math225/daniel/5-3.html (336 words)

	Confidence Interval for a Two-Sample Mean Difference (Site not responding. Last check: 2007-10-22)
		Example #1 constructs a two-sample confidence interval to compare the mean forward and backward change in balance between elderly and young test subjects.
		Exercise #1 constructs a two-sample confidence interval to compare the mean weights of members on the Cambridge and Oxford crew teams.
		Exercise #2 constructs a two-sample confidence interval on the mean specific power difference of land and carrier-based aircraft.
	www.stat.wvu.edu /SRS/Modules/CI_mu1_mu2/ci_mu1_mu2.html (239 words)

	Distribution of Sample Mean
		This handout discusses the distribution of the sample mean and sample sum (they are linear transformations of each other).
		Using the rules for linear transformations, the mean of the sample sum is
		Notice the mean and variance of Y are np and np(1-p), as we derived when discussing Binomial random variables.
	www.ms.uky.edu /~viele/sta281s97/sampdist/sampdist.html (742 words)

	Eco 72 - Homework Assignment 5 (Site not responding. Last check: 2007-10-22)
		A researcher collects a (hopefully) random sample of 144 households in New York state, and finds that the mean number of people in the households in her sample is 2.49.
		In a sample of 169 Netherlands Antilles women, the mean income is 1620 guilders, and the standard deviation of income is 260 guilders.
		A sample of 196 garment workers in Nepal finds that the mean income in the sample was 18,450 rupees and the standard deviation was 3660 rupees.
	phoenix.liu.edu /~tbarr/eco72/eco72-hw05.html (253 words)

	Chapter 7 The Sampling Distribution of the Sample Mean (Site not responding. Last check: 2007-10-22)
		Chapter 7 The Sampling Distribution of the Sample Mean
		Suppose that a variable X of a population is normally distributed with mean m and standard deviation s.
		Obtain the sampling distribution of the sample mean for samples of size
	www.math.niu.edu /~hzhang/stat301/Chap07/03.htm (215 words)

	Sample size computation for multiple comparisons (Site not responding. Last check: 2007-10-22)
		Traditional sample size computation based on "power" does not apply directly to multiple comparisons, because the power of a test of homogeneity includes the probability of an incorrect decision.
		For example, the F-test may reject because the sample mean of treatment 2 is much larger than the sample mean of treatment 3, when in fact the population mean of treatment 2 is smaller than the population mean of treatment 3.
		In a paper titled "On an Approach to Sample Size Determination for Confidence Intervals Proposed by Hsu" which appeared in the JSM97 proceedings of the Biopharmaceutical Section, Olivier Guilbaud of Astra gave a technique to easily and accurately approximate the desired sample size.
	www.stat.ohio-state.edu /~jch/ssinput.html (394 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		This applet simulates finding confidence intervals for the mean of a normal random variable.
		A sample of size 20 is generated from a standard normal random variable.
		The sample mean X and sample standard deviation s are found and used to calculate the confidence interval
	www.math.csusb.edu /faculty/stanton/m262/confidence_means/confidence_means.html (45 words)

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