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Does the confidence interval always contain the true population parameter?
Wiki User
∙ 14y ago
No, the confidence interval (CI) doesn't always contain the true population parameter. A 95% CI means that there is a 95% probability that the population parameter falls within the specified CI.
Wiki User
∙ 14y ago
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What is Confidence Intervals of Degree of Confidence?
, the desired probabilistic level at which the obtained interval will contain the population parameter.
What is the most controllable method of increasing the precision of or narrowing the confidence interval?
Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.
What does 95 percent confidence interval mean?
You construct a 95% confidence interval for a parameter such as mean, variance etc. It is an interval in which you are 95 % certain (there is a 95 % probability) that the true unknown parameter lies. The concept of a 95% Confidence Interval (95% CI) is one that is somewhat elusive. This is primarily due to the fact that many students of statistics are simply required to memorize its definition without fully understanding its implications. Here we will try to cover both the definition as well as what the definition actually implies. The definition that students are required to memorize is: If the procedure for computing a 95% confidence interval is used over and over, 95% of the time the interval will contain the true parameter value. Students are then told that this definition does not mean that an interval has a 95% chance of containing the true parameter value. The reason that this is true, is because a 95% confidence interval will either contain the true parameter value of interest or it will not (thus, the probability of containing the true value is either 1 or 0). However, you have a 95% chance of creating one that does. In other words, this is similar to saying, "you have a 50% of getting a heads in a coin toss, however, once you toss the coin, you either have a head or a tail". Thus, you have a 95% chance of creating a 95% CI for a parameter that contains the true value. However, once you've done it, your CI either covers the parameter or it doesn't.
Why does margin of error increases while level of confidence increases?
The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.
Why is a double line graph used?
Double lined graphs are used to compare two different variables. For example: The x-axis could contain years. The y-axis could contain an amount for a population. The points on the graphs could contain men and women.
What is Confidence Intervals of Degree of Confidence?
, the desired probabilistic level at which the obtained interval will contain the population parameter.
What is the most controllable method of increasing the precision of or narrowing the confidence interval?
Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.
What does 95 percent confidence interval mean?
You construct a 95% confidence interval for a parameter such as mean, variance etc. It is an interval in which you are 95 % certain (there is a 95 % probability) that the true unknown parameter lies. The concept of a 95% Confidence Interval (95% CI) is one that is somewhat elusive. This is primarily due to the fact that many students of statistics are simply required to memorize its definition without fully understanding its implications. Here we will try to cover both the definition as well as what the definition actually implies. The definition that students are required to memorize is: If the procedure for computing a 95% confidence interval is used over and over, 95% of the time the interval will contain the true parameter value. Students are then told that this definition does not mean that an interval has a 95% chance of containing the true parameter value. The reason that this is true, is because a 95% confidence interval will either contain the true parameter value of interest or it will not (thus, the probability of containing the true value is either 1 or 0). However, you have a 95% chance of creating one that does. In other words, this is similar to saying, "you have a 50% of getting a heads in a coin toss, however, once you toss the coin, you either have a head or a tail". Thus, you have a 95% chance of creating a 95% CI for a parameter that contains the true value. However, once you've done it, your CI either covers the parameter or it doesn't.
Why does margin of error increases while level of confidence increases?
The margin of error increases as the level of confidence increases because the larger the expected proportion of intervals that will contain the parameter, the larger the margin of error.
What are quantitative techniques?
Many of the quantitative techniques fall into two broad categories: # Interval estimation # Hypothesis tests Interval Estimates It is common in statistics to estimate a parameter from a sample of data. The value of the parameter using all of the possible data, not just the sample data, is called the population parameter or true value of the parameter. An estimate of the true parameter value is made using the sample data. This is called a point estimate or a sample estimate. For example, the most commonly used measure of location is the mean. The population, or true, mean is the sum of all the members of the given population divided by the number of members in the population. As it is typically impractical to measure every member of the population, a random sample is drawn from the population. The sample mean is calculated by summing the values in the sample and dividing by the number of values in the sample. This sample mean is then used as the point estimate of the population mean. Interval estimates expand on point estimates by incorporating the uncertainty of the point estimate. In the example for the mean above, different samples from the same population will generate different values for the sample mean. An interval estimate quantifies this uncertainty in the sample estimate by computing lower and upper values of an interval which will, with a given level of confidence (i.e., probability), contain the population parameter. Hypothesis Tests Hypothesis tests also address the uncertainty of the sample estimate. However, instead of providing an interval, a hypothesis test attempts to refute a specific claim about a population parameter based on the sample data. For example, the hypothesis might be one of the following: * the population mean is equal to 10 * the population standard deviation is equal to 5 * the means from two populations are equal * the standard deviations from 5 populations are equal To reject a hypothesis is to conclude that it is false. However, to accept a hypothesis does not mean that it is true, only that we do not have evidence to believe otherwise. Thus hypothesis tests are usually stated in terms of both a condition that is doubted (null hypothesis) and a condition that is believed (alternative hypothesis). Website--http://www.itl.nist.gov/div898/handbook/eda/section3/eda35.htmP.s "Just giving info on what you don't know" - ;) Sillypinkjade----
Fiducial Limits in Microbiological Assay?
fiducial limits are similar to confidence limits. They contain the parameter of interest. But i m also not sure of the difference between the 2 limits. And the interpretation is same wether it's microbio or chem or bio.
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