Estimate a population parameter

A parameter is a characteristic of a population. Estimation procedures for two populations The estimation procedures can be extended to two populations for comparative studies.

A population is a group of phenomena that have something in common. For example, suppose a study is being conducted to determine differences between the salaries paid to a population of men and a population of women.

Some confidence intervals would include the true population parameter; others would not. Answer The population is all 7 million college students in the United States today.

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Now is based on a sample, and unless we got really lucky, chances are the. On the average, a random variable misses the mean by one SD. The logic of sampling gives you a way to test conclusions about such groups using only a small portion of its members. When the margin of error is small, the confidence level is low.

For qualitative variables, point and interval estimates of the difference between population proportions can be constructed by considering the difference between sample proportions. The confidence level describes the likelihood that a particular sampling method will produce a confidence interval that includes the true population parameter.

Because samples are manageable in size, we can determine the actual value of any statistic. An interval estimate is defined by two numbers, between which a population parameter is said to lie. We use the known value of the sample statistic to learn about the unknown value of the population parameter.

Populations, Samples, Parameters, and Statistics

For sufficiently large sample sizes, the sample means will be normally distributed about the population mean. For instance, interval estimation of a population variancestandard deviation, and total can be required in other applications.

Confidence intervals are preferred to point estimates, because confidence intervals indicate a the precision of the estimate and b the uncertainty of the estimate. The parameter of interest is p, the proportion of students at Penn State University who 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, multiplying the sample size by a certain factor divides the SE of by the squareroot of that factor. This observation forms the basis for procedures used to select the sample size.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.

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.

Estimation in Statistics

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.

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.

The point estimate for a population parameter is the sample statistic — sample mean estimates population mean, sample proportion estimates population proportion, and so on.

But x̅ and p̂ vary from one sample to the next, so your estimate for μ or p must be a range. 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 .

Estimate a population parameter
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