As Sample Size Increases The Standard Error Of M
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The Larger The Sample Size The Smaller The Standard Error
n is in the denominator of the standard error formula, the standard error decreases as n increases. It makes sense that having more data gives less variation (and more precision) in your results.
Distributions of times for 1 worker, 10 workers, and 50 workers. Suppose X is the time it takes for a clerical worker to type and send one letter of recommendation, and say X the standard error of the mean decreases when has a normal distribution with mean 10.5 minutes and standard deviation 3 minutes. The bottom curve in the preceding figure shows the distribution of X, the individual times for all clerical workers in the population. According to the Empirical Rule, almost all of the values are within 3 standard deviations of the mean (10.5) -- between 1.5 and 19.5. Now take a random sample of 10 clerical workers, measure their times, and find the average, each time. Repeat this process over and over, and graph all the possible results for all possible samples. The middle curve in the figure shows the picture of the sampling distribution of Notice that it's still centered at 10.5 (which you expected) but its variability is smaller; the standard error in this case is (quite a bit less than 3 minutes, the standard deviation of the individual times). Looking at the figure, the average times for samples of 10 clerical workers are closer to the mean (10.5) than the individual times are. That's because average times don't vary as much from sample to sample as individual times vary from person to person. Now take all possible random samples of 50 clerical workers andthe following questions in one or two well-constructed sentences. a. What happens to the standard error of a sampling distribution as good standard error values the size of the sample increases? b. Log On Ad: Mathway
One Standard Error Of The Mean
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As Sample Size Increases The Standard Deviation
math help from PAID TUTORS. (paid link) Click here to see ALL problems on Probability-and-statistics Question 648031: Answer the following questions in one or two well-constructed sentences. http://www.dummies.com/education/math/statistics/how-sample-size-affects-standard-error/ a. What happens to the standard error of a sampling distribution as the size of the sample increases? b. What happens to the distribution of the sample means if the sample size in increased? c. When using the distribution of sample means to estimate the population mean, what is the benefit of using larger sample sizes? http://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.648031.html Answer by Theo(7031) (Show Source): You can put this solution on YOUR website! as the size of the sample increases, the standard error decreases. standard error equals standard deviation of population divided by square root of sample size. bigger sample size means bigger denominator resulting in smaller standard error. if the sample size increases, the distribution of sample means becomes more normal. this is the main idea of the central limit theorem. even if the population distribution is not normal, the distribution of sample means becomes more normal the larger the sample size. the benefit of larger sample sizes is that the mean of the sample will be closer to the actual population mean and the standard error will be less. the sample mean will be closer to the population mean because the sample size is larger. this also results in a smaller standard error. this also results in a more normal distribution which increases the accuracy of using the z-tables when determing dev
using Windows 95, 98 or NT. When asked if you want to install the sampling control, click on Yes. When we draw a sample from a population, and calculate a sample statistic such as the mean, http://academic.udayton.edu/gregelvers/psy216/activex/sampling.htm we could ask how well does the sample statistic (called a point estimate) represent the same value for the population? That is, if we calculate the mean of a sample, how close will it be to the mean of the population? Of course, the answer will change depending on the particular sample that we draw. But could we develop a measure that would at least give us an indication standard error of how well we expect the sample mean to represent the population mean? We could subtract the sample mean from the population mean to get an idea of how close the sample mean is to the population mean. (Technically, we don't know the value of the population mean -- if we knew the population mean, then there would be no sense in calculating the sample mean. But in theory, it the standard error is possible to get an arbitrarily good estimate of the population mean and we can use that estimate as the population mean.) That is, we can calculate how much the sample mean deviates from the population mean. But is this particular sample representative of all of the samples that we could select? It may or may not be. So, we should draw another sample and determine how much it deviates from the population mean. In fact, we might want to do this many, many times. We could then calculate the mean of the deviates, to get an average measure of how much the sample means differ from the population mean. The standard error of the mean does basically that. To determine the standard error of the mean, many samples are selected from the population. For each sample, the mean of that sample is calculated. The standard deviation of those means is then calculated. (Remember that the standard deviation is a measure of how much the data deviate from the mean on average.) The standard deviation of the sample means is defined as the standard error of the mean. It is a measure of how well the point estimate (e.g. the sample mean) represents the population paramet