1.645 Standard Error
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Z Score For 95 Confidence Interval
works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top When to use a t value and when to use 1.645 for a 90% confidence interval? up vote 1 down vote favorite 2 The question I am working with is: Setup a 90% confidence interval estimate for the average processing time. I gathered the information z score for 80 confidence interval below from the spreadsheet $n = 27$ $\bar{X} =48.888$ Sample standard deviation $= 25.283$ $\sigma/\sqrt{n} = 4.871$ I am confused because I thought that to setup the confidence level I would use 1.645 which is a common level confidence for the 90% confidence level. My final answer was: We are 90% confident that the average processing time is between 40.8 and 56.9 days. My final answer is wrong. I double checked with a excel template and instead of 1.645 the template used a t value calculated using an exel function called TINV which I am not sure how to calculate. Any help would be greatly appreciated. confidence-interval share|improve this question edited May 31 '12 at 7:34 asked May 31 '12 at 6:25 Filype 1255 add a comment| 1 Answer 1 active oldest votes up vote 7 down vote accepted You should use $\bar{X}\pm\sigma z_{1-\alpha/2}/\sqrt{n}$ where $z_{1-\alpha/2}$ is normal quantile when population standard deviation $\sigma$ is known. In your case you have only estimate $\hat\sigma$, therefore you should use $\bar{X}\pm\sigma t_{1-\alpha/2}(n-1)/\sqrt{n}$ where $t_{1-\alpha/2}(n-1)$ is student quantile with $n-1$ degrees of freedom (TINV(1-0.9,27-1)=1.706 function in Excel). So you obtain wider confidence interval - more un
estimated range being calculated from a given set of sample data. (Definition taken from Valerie J. Easton and John H. McColl's Statistics Glossary v1.1) The common notation for the parameter in 99 confidence interval t score question is . Often, this parameter is the population mean , which is
90 Confidence Interval T Value
estimated through the
Z Score For 90 Percent Confidence Interval
interval produced by the method employed includes the true value of the parameter . Example Suppose a student measuring the boiling temperature of a certain liquid observes the readings (in degrees Celsius) http://stats.stackexchange.com/questions/29538/when-to-use-a-t-value-and-when-to-use-1-645-for-a-90-confidence-interval 102.5, 101.7, 103.1, 100.9, 100.5, and 102.2 on 6 different samples of the liquid. He calculates the sample mean to be 101.82. If he knows that the standard deviation for this procedure is 1.2 degrees, what is the confidence interval for the population mean at a 95% confidence level? In other words, the student wishes to estimate the true mean boiling temperature of the http://www.stat.yale.edu/Courses/1997-98/101/confint.htm liquid using the results of his measurements. If the measurements follow a normal distribution, then the sample mean will have the distribution N(,). Since the sample size is 6, the standard deviation of the sample mean is equal to 1.2/sqrt(6) = 0.49. The selection of a confidence level for an interval determines the probability that the confidence interval produced will contain the true parameter value. Common choices for the confidence level C are 0.90, 0.95, and 0.99. These levels correspond to percentages of the area of the normal density curve. For example, a 95% confidence interval covers 95% of the normal curve -- the probability of observing a value outside of this area is less than 0.05. Because the normal curve is symmetric, half of the area is in the left tail of the curve, and the other half of the area is in the right tail of the curve. As shown in the diagram to the right, for a confidence interval with level C, the area in each tail of the curve is equal to (1-C)/2. For a 95% confidence interval, the area in each tail is equal to
Deviation and DestributionsOriginally posted at http://www.howtomeasureanything.com, on Tuesday, February 03, 2009 9:20:28 AM, by lascar. "Hello. I've enjoyed the book and am trying to apply AIE to some of our IT decision making. Unfortunately I https://www.hubbardresearch.com/standard-deviation-and-destributions/ don't have a statistician's background and my college days are quite far away. So, [I'm] trying to catch up on some basics. Wikipedia is amazingly helpful in this sense. I have two questions. If they are two basic for this forum, I'd appreciate anyone at least directing me to some resources which might help me answer them. Direct answers of cause confidence interval are even more welcomed. 1. In Monte Carlo example in the book, the assumption is that most of the variables have Normal distribution. And if not, there are 2 more distributions mentioned - Uniform and Binary. I guess these are most common? My question is: how does one quickly evaluate what type of distribution is fitting for a variable? I'd guess 99 confidence interval it is quite straight forward with binary distribution. However from this article (http://en.wikipedia.org/wiki/List_of_probability_distributions), it seams there is quite a choice of distributions. The MC scenario I'm running is to evaluate performance of a software package. I also realize that a quick proof of concept (running software and collecting metrics) might shed more light on distribution of some metric/variable. However that requires acquiring an expensive license first. So the decision I'm trying to facilitate is to prove that we need a POC and I need to calculate the value of improving on these measurements with POC's help - alas - that cost of POC is worth lowering the uncertainty of measurements. 2. In the same Monte Carlo example standard deviation of 3.29 is used and the statement is that it is for 90% CI. However I've stumbled on this article (http://en.wikipedia.org/wiki/Standard_deviation#Rules_for_normally_distributed_data) and it seams the standard deviation for 90% is 1.645. 3.49 is closer to 99% CI. Can someone clarify, please? Thank you." Thanks for your interest. First, yes there are quite a few distributions to choose from. I included the thre
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