Week 8- Confidence Intervals, Population Proportions, and Population Means Flashcards
Point Estimator
A statistic that provides an estimate of a population parameter.Functions that are used to find an approximate value of a population parameter from random samples of the population. They use the sample data of a population to calculate a point estimate or a statistic that serves as the best estimate of an unknown parameter of a population.
Point Estimate
The value of the point estimator statistic. It is our best educated guess of the value of an unknown parameter. the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a “best guess” or “best estimate” of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate.
Confidence Interval
An interval estimating a population parameter, in the form 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒 ±
𝑚𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑒𝑟𝑟𝑜𝑟, which has two parts: Margin of Error and Confidence Level C. the mean of your estimate plus and minus the variation in that estimate. This is the range of values you expect your estimate to fall between if you redo your test, within a certain level of confidence. Confidence, in statistics, is another way to describe probability
Margin of Error
Tells us how close the estimate tends to be to the unknown parameter
in repeated random sampling. The margin of error is a way to express how much the results of a survey or poll could differ from the actual truth. It’s a tool used in statistics to show the level of uncertainty in the data.
Confidence Level C
The overall success rate for the method of calculating the confidence interval. In C% of all possible samples, the method would yield an interval which captures the true parameter value. The probability that a population parameter will fall between a set of values for a certain proportion of times. Analysts often use confidence intervals that contain either 95% or 99% of expected observations
Standard Error
The result when the standard deviation of a statistic is estimated from data. a measure of the variability or spread of a statistic (like the sample mean) across multiple samples drawn from the same population. It helps determine how much the sample mean is likely to deviate from the true population mean, and it’s used to construct confidence intervals and perform hypothesis tests.
t Distribution
A distribution formed when we standardize a random variable using the samples’ standard deviations rather than a known population standard deviation. A way of describing a set of observations where most observations fall close to the mean, and the rest of the observations make up the tails on either side. a way of describing data that follow a bell curve when plotted on a graph, with the greatest number of observations close to the mean and fewer observations in the tails.
It is a type of normal distribution used for smaller sample sizes, where the variance in the data is unknown.
Degree of Freedom
The number of values in a system which may vary; in a practical sense, when working with t distributions, it is one less than the sample size. (often abbreviated as df) refers to the number of independent pieces of information used to calculate a statistic, essentially the number of values in a calculation that are free to vary. In inferential statistics, you estimate a parameter of a population by calculating a statistic of a sample. The number of independent pieces of information used to calculate the statistic is called the degrees of freedom. The degrees of freedom of a statistic depend on the sample size:
When the sample size is small, there are only a few independent pieces of information, and therefore only a few degrees of freedom.
When the sample size is large, there are many independent pieces of information, and therefore many degrees of freedom. Although degrees of freedom are closely related to sample size, they’re not the same thing. There are always fewer degrees of freedom than the sample size.
Standard Error of the Sample Mean
Sample standard deviation divided by the square root of the sample size; It describes how far 𝑥̅ will be from 𝜇, on average, in repeated SRSs of size n. indicates how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.
Robust
An inference procedure is called “robust” if the probability calculations involved in that procedure remain fairly accurate when a condition for using that procedure is violated.The ability of a method or test to perform consistently well, even when the underlying assumptions or data conditions are not perfectly met, such as when outliers or deviations from normality are present
