population

Examples of population in the following topics:

• Populations

  • This is one type of population.
  • A statistical population is a set of entities from which statistical inferences are to be drawn, often based on a random sample taken from the population.
  • This type of information gathering over a whole population is called a census .
  • A subset of a population is called a sub-population.
  • If different sub-populations have different properties, so that the overall population is heterogeneous, the properties and responses of the overall population can often be better understood if the population is first separated into distinct sub-populations.

• Summary of Types of Hypothesis Tests

  • Populations are independent and population standard deviations are known (not likely).

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation known.
  • Conduct and interpret hypothesis tests for a single population mean, population standard deviation unknown.

• Student Learning Outcomes

  • Conduct and interpret hypothesis tests for two population means, population standard deviations known.
  • Conduct and interpret hypothesis tests for two population means, population standard deviations unknown.

• Summary

  • A One-Way ANOVA hypothesis test determines if several population means are equal.
  • Each population from which a sample is taken is assumed to be normal.
  • The populations are assumed to have equal standard deviations (or variances)
  • The populations from which the two samples are drawn are normally distributed.

• Assumption

  • You use the sample standard deviation to approximate the population standard deviation.
  • When you perform a hypothesis test of a single population mean µ using a normal distribution (often called a z-test), you take a simple random sample from the population.
  • The population you are testing is normally distributed or your sample size is sufficiently large.
  • You know the value of the population standard deviation.
  • When you perform a hypothesis test of a single population proportion p, you take a simple random sample from the population.

• Estimating a Population Proportion

  • In order to estimate a population proportion of some attribute, it is helpful to rely on the proportions observed within a sample of the population.
  • In order to estimate the proportions of some attribute within a population, it would be helpful if you could rely on the proportions observed within a sample of the population.
  • While the sample proportion might be the best estimate of the total population proportion, you would not be very confident that this is exactly the population proportion.
  • This leads to an estimate of 52% as $A$'s support in the population.
  • The population proportion, $p$, is estimated using the sample proportion $\hat{p}$.

• Variance

  • In describing a complete population, the data represents all the elements of the population.
  • When determining the spread of the population, we want to know a measure of the possible distances between the data and the population mean.
  • A clear distinction should be made between dealing with the population or with a sample from it.
  • When dealing with the complete population the (population) variance is a constant, a parameter which helps to describe the population.
  • The population variance can be very helpful in analyzing data of various wildlife populations.

• Using Two Samples

  • Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population.
  • The parameter tested using matched pairs is the population mean (see ).
  • The parameters tested using independent groups are either population means or population proportions.
  • Tests of matched or paired samples (necessarily a test of the population mean)
  • In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means.

• Distribution Needed for Hypothesis Testing

  • Perform tests of a population mean using a normal distribution or a student's-t distribution.
  • If you are testing a single population mean, the distribution for the test is for means:
  • The population parameter is µ.
  • If you are testing a single population proportion, the distribution for the test is for proportions or percentages:
  • The population parameter is p.