90 Confidence Standard Error
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we that the true population average is in the shaded area? We are 95% confident. This is the level of confidence. How many standard 90 confidence interval standard deviation errors away from the mean must we go to be 95% confident? From standard error confidence interval calculator -z to z there is 95% of the normal curve. There are 4 typical levels of confidence: 99%, 98%, 95%
Standard Error Of Measurement Confidence Interval
and 90%. Each of the levels of confidence has a different number of standard errors associated with it. We denote this by where a is the total amount of area in the tails
Margin Of Error Confidence Interval
of the normal curve. Thus, for a 95% level of confidence . Level of confidence1-a a/2 90% 5% 1.645 95% 2.5% 1.96 98% 1% 2.33 99% 0.5% 2.575 How do we compute a confidence interval. After selecting (or being told) that level of confidence, for a large (n>30) sample we use the formula . example: A sample of 100 observations is collected and yields m=75 and s=8. sampling error confidence interval Find a 95% confidence interval for the true population average. = = =(73.432,76.568). For a sample of 121 observations with an average of 50 and standard deviation of 20, find a 90% confidence interval for the true population average. Kennesaw State University claims the average starting salary of its graduates is $38,500. A sample of 100 KSU students is sampled and yields an average starting salary of $36,800 with a standard deviation of $9,369. Using a 95% confidence level what can you say about KSU's claim? Homework Section 6-3: 3, 4, 9, 10, 12, 21-23 For samples that are not large (i.e. small) we make one correction. We use a t-chart to replace the normal curve chart and use the formula . example: Find a 99% confidence interval for the true population average from which the sample S={229, 255, 280, 203, 229} is randomly selected. First we compute the average and standard deviation of the sample. The average is 239.2 and the standard deviation is 29.3. Thus, =. degrees of freedom = n-1 Thus, . ==(178.9,299.5) [SyllabusFiles] [TipsforSuccess] [Intro] [Chapter2:NumericalMethods] [Chapter3:Probability] [Chapter4:ProbabilityDistributions] [Chapter5:TheNormalCurve] [Chapter5:CentralLimitTheorem] [Chapter4:TheBinomialProbabilityDistribution] [Questionnaire] [Chapter1] [Chapter6:ConfidenceIntervals] [Chapter6:RequiredSampleSize] [Chapter6:EstimationofProportion] [RequiredSampleSize(Update
Software To Calculate Confidence Intervals Print Lesson Confidence Intervals Constructing confidence intervals to estimate a population proportion NOTE: the following interval calculations for the proportion confidence interval is dependent on the following assumptions being satisfied: np ≥ 10 and n(1-p) ≥ 10. If
95 Confidence Standard Deviation
p is unknown then use the sample proportion. The goal is to estimate p = standard error p value proportion with a particular trait or opinion in a population. Sample statistic = (read "p-hat") = proportion of observed sample with the trait or standard error hypothesis testing opinion we’re studying. Standard error of , where n = sample size. Multiplier comes from this table Confidence Level Multiplier .90 (90%) 1.645 or 1.65 .95 (95%) 1.96, usually rounded to 2 .98 (98%) 2.33 .99 (99%) 2.58 http://science.kennesaw.edu/~jdemaio/1107/Chap6.htm The value of the multiplier increases as the confidence level increases. This leads to wider intervals for higher confidence levels. We are more confident of catching the population value when we use a wider interval. Example In the year 2001 Youth Risk Behavior survey done by the U.S. Centers for Disease Control, 747 out of n = 1168 female 12th graders said the always use a seatbelt when driving. Goal: Estimate proportion always using seatbelt when driving in http://stat.psu.edu/~ajw13/stat200_upd/07_CI/03_CI_CI.htm the population of all U.S. 12th grade female drivers. Check assumption: (1168)*(0.64) = 747 and (1168)*(0.36) = 421 both of which are at least 10. Sample statistic is = = 747 / 1168 = .64 Standard error = A 95% confidence interval estimate is .64 ± 2 (.014), which is .612 to .668 With 95% confidence, we estimate that between .612 (61.2%) and .668 (66.8%) of all 12th grade female drivers always wear their seatbelt when driving. Example Continued: For the seatbelt wearing example, a 99% confidence interval for the population proportion is .64 ± 2.58 (.014), which is .64 ± .036, or .604 to .676. With 99% confidence, we estimate that between .604 (60.4%) and .676 (67.6%) of all 12th grade female drivers always wear their seatbelt when driving. Notice that the 99% confidence interval is slightly wider than the 95% confidence interval. IN the same situation, the greater the confidence level, the wider the interval. Notice also, that the only the value of the multiplier differed in the calculations of the 95% and 98% intervals. Using Confidence Intervals to Compare Groups A somewhat informal method for comparing two or more populations is to compare confidence intervals for the value of a parameter. If the confidence intervals do not overlap, it is reasonable to conclude that the parameter value differs for the two populations. Example In the Youth Risk Behavior s
test AP formulas FAQ AP study guides AP calculators Binomial Chi-square f Dist Hypergeometric Multinomial Negative binomial Normal Poisson t Dist Random http://stattrek.com/estimation/margin-of-error.aspx numbers Probability Bayes rule Combinations/permutations Factorial Event counter Wizard Graphing Scientific Financial Calculator books AP calculator review Statistics AP study guides Probability Survey sampling Excel Graphing calculators Book reviews Glossary AP practice exam Problems and solutions Formulas Notation Share with Friends Margin of Error In a confidence interval, the range of values above standard error and below the sample statistic is called the margin of error. For example, suppose we wanted to know the percentage of adults that exercise daily. We could devise a sample design to ensure that our sample estimate will not differ from the true population value by more than, say, 5 percent (the margin of error) error confidence interval 90 percent of the time (the confidence level). How to Compute the Margin of Error The margin of error can be defined by either of the following equations. Margin of error = Critical value x Standard deviation of the statistic Margin of error = Critical value x Standard error of the statistic If you know the standard deviation of the statistic, use the first equation to compute the margin of error. Otherwise, use the second equation. Previously, we described how to compute the standard deviation and standard error. How to Find the Critical Value The critical value is a factor used to compute the margin of error. This section describes how to find the critical value, when the sampling distribution of the statistic is normal or nearly normal. The central limit theorem states that the sampling distribution of a statistic will be nearly normal, if the sample size is large enough. As a rough guide, many statisticians say that a sample