What do confidence intervals represent?
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When you compute a mean from a sample, you are estimating the mean of the population from which you sampled.  The population mean is sometimes refered to as the true mean and the mean you compute from your sample is called the sample mean.\n\nWith repeated sampling, you'll come up with a different sample mean each time.  This distribution of sample means is refered to as the sample distribution and it is approximately Normal in distribution.\n\nWhen you compute the standard error using the standard deviation and the sample size, you are estimating the variability in the sample mean.\n\nWhen you estimate confidence intervals, you are estimating the range of possible values where the population may lie relative to your sample mean.\n\nFor instance, your sample mean plus or minus 1.96 standard errors represents an estimate of the 95% confidence interval or range that may contain the population mean relative to your sample mean.  There is a 5% chance that the population mean is actually higher or lower than this range.\n\nLet's say you toss a coin twenty times and measure 9 heads and 11 tails.  The average number of coin tosses at 0.45 heads (which implies 0.55 tails).  The standard error estimate is 0.055343. Multipling the standard error estimate by 1.96 and adding and subtracting the result from the mean yields our 95% confidence interval. There is a 95% chance that the population mean for this process is between 0.341528 and 0.558472.
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For one-sample t-test, \nt = (sample mean - population mean) / estimated standard error. \n\nIn math notation, t = (X bar - mu not) / (s/sqrt(n))\n\nAssumptions: (normal population or sample size, n, is at least 30) and population standard deviation is unknown.\n\nThere are other variations of t-tests like two-sample(pooled and unpooled) and paired ...
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Approximately 95% of the data is within 2 standard deviations of the mean.\nCheck out this website\nhttp://en.wikipedia.org/wiki/Confidence_interval\nand look under the section\n"Confidence Intervals in Measurement"
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The confidence interval will be for the average rate or the unobservable rate.
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Standard deviation tells you the spread of the data, for example the data may be very close together or very spread out.\n\nConfidence limits tell you how accurate a particular model or hypothesis test is\n\nQ-test tells you about extreme values\n\nPolled standard deviation is the standard deviation of the sample of data, not necessarily the same as the actual standard deviation
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population sample size (n) = 12\nsquare root of sample size = 3.464\nmean of the data = 11.692\nstandard deviation = .777\n\nIt's too hard to type in math notation so, in words, use the formula: \nmean plus or minus critical k-value multiplied by (standard deviation divided by the square-root of n)\n\nSo for your example, it would be:\n11.692 +/- k(.777/3.464) --> take .777 divided by 3.464\n= 11.692 +/- k(.224) so solving for k -->\n11.692 + k(.224) = 13 \nk = 5.84 \n11.692 - k(.224) = 10\nk = 7.6\n\nThis formula is for the confidence interval for the mean of a normal population. It assumes that this was a simple random sample and is just one of the formulas that you could possibly use. You didn't specify if the data was Normally distributed (I'm not going to check and do everything for you). Just to put this answer in perspective, a confidence level of 99.9 % corresponds to a "k-value" of 3.291
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confidence intervals are about what % confident you are that a given person's score falls between x score and x score on any given day.  formulas: \n\n                                   68% CI=X+/-1(Standard error of measurement)\n                                   95%CI=X+/-1.96(SEM)\n                                   98%CI=X+/-2.58(SEM)\n\nto get the SEM:  SD(standard deviation)times the square root of 1 minus the reliability coefficient(rtt)\n\nI might be wrong about the margin of error, but I think it's the SEM(the index of the amount of error that can be expected in obtained test scores due to the unreliability of the test) \n\nhope this helps--statistics suck!
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Parametric and Non-Parametric data\n\nIn statistical terms a parameter is a statistic calculated from a set of data, e.g. a mean or a standard deviation are both parameters. In order to calculate parameters, and to use them in statistical analysis three assumptions must be tested against the data. The data is considered as parametric if these three assumptions are valid:\n\n1. Can it be assumed that the data has been obtained from a population which is considered "normal" in the statistical sense. In other words if a sufficiently large sample of data was obtained from the population is it likely that it would be normally distributed. This may be known from similar research, but if not, and provided the sample is reasonably large, it may be possible to estimate from the sample whether this assumption is reasonable.\n\n2. The populations from which the samples are drawn should have equal variances. This can be determined by inspection of the data, looking at the spread or standard deviation of the data. The F - test can also be used to test the hypothesis that the samples have been drawn from populations with the equal variance.\n\n3. The data should be measured, at the very least, on an interval scale. Even this is not always easy to determine, but a useful "rule of thumb" is to compare two scores, (say) a 5 and a 10, and to ask yourself if a score of 10 means that there is exactly twice as much of that particular attribute compared with a score of 5. If the data was temperature, then this is obviously the case, but what if the data represented a measure of patient satisfaction. A score of 10 may indicate more satisfaction than a 5, but not necessarily twice as much; i.e. this may be an ordinal scale rather than interval.\n\nIt is not always easy to know whether the data should be treated as parametric or non-parametric, and where possible always look at how other researcher have treated similar data. Of course it does not follow that they were correct in their assumptions, but at least if the research has been published, it will have been scrutinised by other researchers.\n\nA further complication is that some statistical tests, e.g. the t - test is considered as "robust". This means that even if one of the assumptions is doubtful, then it is still possible to use the t - test.\n\nIf you have any doubts about the nature of your data, then it is safer to opt for the non-parametric test, because they do not require these assumptions of the data. Non-parametric tests are a little less sensitive than their parametric equivalent, and therefore they may not detect small differences between groups. You can't go wrong choosing a non-parametric test, but you may be accused of using the wrong sort of test if you choose a parametric test, when the nature of the data does not warrant it.
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Look at the table of values for the normal distribution.  95% of the values are included within +/- 1.9 SD of the mean.  So:  1.9 x 6.2 = 11.78 and the interval is\n\n     26 - 11.78 <= Mean <= 26 + 11.78, or\n           14.22<= Mean >= 37.78
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Finance:\nStandard deviation might be used to characterize how much spread to expect in a group of investments.  High standard deviation implies high uncertainty.\n\nManufacturing:\nLikewise for manufactured parts.  High standard deviation here means highly variable parts.  Manufacturers was low variability, so that parts fit together well.\n\nMedicine:\nA drug might be tested and shown to reduce blood pressure.  If the amount of reduction has a high standard deviation, though, the drug may not be reliable.
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The mean describes the average score, the SD describes the shape and range of the normal distribution, or bell curve. \nWith this information, we can say the following:\nAbout 68% of test-takers got between 65% and 73%- a very tight grouping (the area within 1 SD).  Approximately 95% of people got between 61% and 77% (2 SD), and about 98-99% got between 57% and 81% (a range of 3 standard deviations).
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Standard deviation tells you how spread out a set of numbers is.  A small standard deviation means that the numbers are close together.  A large one says that they're far apart.\n\nIt's often used as a measure of distance away from the mean.  In a normal distribution, about 68% of numbers are within one standard deviation from the mean.  For example, if you have a normal distribution with a mean of 50 and a standard dev of 10, then about 68% of the numbers are between 40 and 60.  And about 95% of the numbers are within two standard deviations, or between 30 and 70.
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Take a set of say, 51 data points of varying values.\n\nArrange them from least to greatest.\n\nThe 26th data point is the mode.\n\nThis is different from the median, which is the sum of the data points divided by 51.  The median will not necessarily be equal to any of the data points, while the mode, by definition, will.  If the distribution is normal, aka a bell curve, the median and the mode will be very close.  If the distribution is not a bell curve then the median and the mode may be quite different.
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It means that there is a large gap in the middle of the data set with one or a small ammount of entries being grossly larger than the majority of the set:\n   the set 1,2,3,4,30 has a mean of 8 and a median of 3\n   the set 20,22,28,32,33,34,64,68,71 has a mean of 49 and \n   a median of 33
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Usually this term is used in parameter estimation. There exists a number (parameter) relative to a population, but you only use a sample of that population to estimate it. You can´t say for sure what the number is, but you can give a confidence interval.\n \nFor example, lets say you want to know the average height of NBA players but only know the height of 50 players. Supposing those 50 players were a random sample, the average of that sample is the best estimate of the average height of all NBA players. Nevertheless, the actual NBA average will likely not be the same. Using the center limit theorem allows you to develop a theory that leads to the confidence interval.\n \nSuppose it turned out that your estimated average was 2.00m and the 95% C.I. was 1.90 - 2.10. What that really means, is that, *if* the actual average is 2.00m, 95% of the time you sample 50 players randomly, the sample average will be in that range. You can turn that statement around (it boggles the mind, I know) and say that, if the actual population is outside the 1.90 - 2.10 interval, the chance of a random sample having a 2.00 average is less than 5%.\n \nIf you really want to understand the why´s and the caveats, you have to get a basic understanding of central limit theorem and draw the normal distribution of the sampled parameter.
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What kind of statistic are you looking for?
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When the population standard deviation is unknown, thats when you use the t-distribution, in calculating the confidence interval. \n\nThe t-distribution (also known as Student's t-distribution) measures the significance of a difference of means of small samples when two distributions are though to have the same variance, but possibly different means.\n\nBut as the sample size increases, the t-distribution gets close to the normal distribution.\n\nHope this helps!