For example, suppose we compute an interval estimate of a population parameter. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions. The estimator should be unbiased, meaning that the expected value of the estimator should be equal to the population parameter.
When the margin of error is small, the confidence level is high. In the formula for the SE ofthe sample size appears i in the denominator, and ii inside a squareroot. Then our estimate is of the graduating class plan to go to graduate school.
Rather, it reflects the amount of random error in the sample and provides a range of values that are likely to include the unknown parameter. A confidence interval consists of three parts. The Central Limit Theorem states that for large samples: Let us focus for now on the sample mean as an estimate of the population mean.
The estimator should be robust, meaning that it is both unbiased and efficient for many different population distributions. The estimator should be efficient, meaning that the standard error of the estimator is relatively small, compared to other possible estimators.
Here is how to interpret a confidence level. A point estimate of a population parameter is a single value of a statistic.
The parameter of interest is p, the proportion of students at Penn State University who smoke regularly. Some confidence intervals would include the true population parameter; others would not.
Interestingly, the population formula for a variance, when performed on a sample, is a biased estimator of the population variance. Interval estimation incorporates a probability statement about the magnitude of the sampling error.
What happens if we do not know anything about a population? As a matter of practice, statisticians usually consider samples of size 30 or more to be large. In order to use statistics to learn things about the population, the sample must be random.
A research question is "what proportion of these students smoke regularly? Now our sample mean will rarely fall at exactly the population mean, but is more likely to be somewhat different, as indicated by the blue triangle below. Therefore, we can use the sample mean distribution about a sample mean rather than about the unknown population mean to generate probabilities that our estimate is correct.
This last term is called the standard error of estimation of the sample proportion, or simply standard error SE of the proportion. Inferential statistics enables you to make an educated guess about a population parameter based on a statistic computed from a sample randomly drawn from that population see Figure 1.
For both continuous and dichotomous variables, the confidence interval estimate CI is a range of likely values for the population parameter based on: A sample is a representative group drawn from the population. By substituting the expression on the right side of the equation: The actual number depends on how you define "college student.
Answer The population is all 7 million college students in the United States today. The statistic and the margin of error define an interval estimate that describes the precision of the method.
The confidence level describes the uncertainty of a sampling method.
Estimation procedures for two populations The estimation procedures can be extended to two populations for comparative studies.In econometrics, when you collect a random sample of data and calculate a statistic with that data, you’re producing a point estimate, which is a single estimate of a population parameter.
Descriptive statistics are measurements that can be used to summarize your sample data and, subsequently, make predictions about your population of interest. Estimating Population Parameters Slide 1 of 5. NOTE: This is a frame enhanced page. Best viewed in a web browser that supports frames (e.g.
Netscape or Internet Explorer). Estimating Population Parameters. Table of Contents Select a slide or start at the beginning.
Estimating Population Parameters. Populations, Samples, Parameters, and Statistics. For example, say you want to know the mean income of the subscribers to a particular magazine—a parameter of a population. You draw a random sample of subscribers and determine that their mean income is $27, (a statistic).
You conclude that the population mean income μ is. There are two types of estimates for each population parameter: the point estimate and confidence interval (CI) estimate. For both continuous variables (e.g., population mean) and dichotomous variables (e.g., population proportion) one first computes the point estimate from a sample.
An estimate of a population parameter may be expressed in two ways: Point estimate. A point estimate of a population parameter is a single value of a statistic.
For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample. Estimating the Population Proportion p The TV World computations in the previous section assume that we know the warranty rate is p In data analysis, population parameters like p are typically unknown and estimated from the data.Download