How To Find Confidence Interval With Standard Error
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95 Confidence Interval Z Score
for the population mean, When the population standard deviation is known, the formula for a confidence interval (CI) for a population mean is deviation, n is the sample size, and z* represents the appropriate z*-value from the standard normal distribution for your desired confidence level. z*-values for Various Confidence Levels Confidence Level z*-value 80% 1.28 90% 1.645 (by convention) 95% 1.96 98% 2.33 99% 2.58 The above table shows values of z* for the given confidence levels. Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used. In this case, the data either have to come from a normal distribution, or if not, then n has to be large enough (at least 30 or so) in order for the Central Limit Theorem to be applied , allowing you to use z*-values in the formula. To calculate a CI for the population mean (average), under these conditions, do the following: Determine the confidence level and find the appropriate z*-value. Refer to the above table. Find the sample mea
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90 Confidence Interval
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distribution used in probability and statistics. 95% of the area under a normal curve lies within roughly 1.96 standard http://en.wikipedia.org/wiki/1.96 deviations of the mean, and due to the central limit theorem, this number is therefore used in the construction of approximate 95% confidence intervals. Its ubiquity is due to http://stattrek.com/estimation/confidence-interval-mean.aspx?Tutorial=AP the arbitrary but common convention of using confidence intervals with 95% coverage rather than other coverages (such as 90% or 99%).[1][2][3][4] This convention seems particularly common in medical confidence interval statistics,[5][6][7] but is also common in other areas of application, such as earth sciences,[8] social sciences and business research.[9] There is no single accepted name for this number; it is also commonly referred to as the "standard normal deviate", "normal score" or "Z score" for the 97.5 percentile point, or .975 point. If X has a standard confidence interval for normal distribution, i.e. X ~ N(0,1), P ( X > 1.96 ) = 0.025 , {\displaystyle \mathrm {P} (X>1.96)=0.025,\,} P ( X < 1.96 ) = 0.975 , {\displaystyle \mathrm {P} (X<1.96)=0.975,\,} and as the normal distribution is symmetric, P ( − 1.96 < X < 1.96 ) = 0.95. {\displaystyle \mathrm {P} (-1.96