Examples of population in the following topics:

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

 Give examples of a statistical populations and subpopulations
In statistics, a population includes all members of a defined group that we are studying for data driven decisions.
 It is often impractical to study an entire population, so we often study a sample from that population to infer information about the larger population as a whole.
 A subset of a population is called a subpopulation.
 A subset of a population is called a subpopulation.
 If different subpopulations 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 subpopulations.
 sample (noun) a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population

 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.
 Conduct and interpret hypothesis tests for two population proportions.

 By the end of this chapter, the student should be able to:
Differentiate between Type I and Type II Errors
Describe hypothesis testing in general and in practice
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.
 Conduct and interpret hypothesis tests for a single population proportion.

 A OneWay ANOVA hypothesis test determines if several population means are equal.
 Assumptions:
Each population from which a sample is taken is assumed to be normal.
 The populations are assumed to have equal standard deviations (or variances)
A Test of Two Variances hypothesis test determines if two variances are the same.
 Assumptions:
The populations from which the two samples are drawn are normally distributed.
 The two populations are independent of each other.

 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 ztest), 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.

 When determining the "spread" of the population, we want to know a measure of the possible distances between the data and the population mean.
 When dealing with the complete population the (population) variance is a constant, a parameter which helps to describe the population.
 In describing a complete population, the data represents all the elements of the population.
 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.

 Recall that the field of Statistics involves using samples to make inferences about populations and describing how variables relate to each other.
 To use a sample as a guide to an entire population, it is important that it truly represent the overall population.
 Populations can be diverse topics such as "all persons living in a country" or "every atom composing a crystal.".
 Data collected about this kind of "population" constitutes what is called a time series.
 To use a sample as a guide to an entire population, it is important that it truly represent the overall population.
 population (noun) a group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn
 sample (noun) a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population

 It might be somewhat lower or higher, but it would not equal the population mean exactly.
 Inferential statistics involves generalizing from a sample to a population.
 For example, consider a normal population with mean μ and variance σ.
 Assume we repeatedly take samples of a given size from this population and calculate the arithmetic mean for each sample.
 " This distribution is normal since the underlying population is normal, although sampling distributions may also often be close to normal even when the population distribution is not.
 inferential statistics (noun) A branch of mathematics that involves drawing conclusions about a population based on sample data drawn from it.

 Perform tests of a population mean using a normal distribution or a student'st distribution.
 (Remember, use a student'st distribution when the population standard deviation is unknown and the distribution of the sample mean is approximately normal.
) In this chapter we perform tests of a population proportion using a normal distribution (usually n is large or the sample size is large).
 If you are testing a single population mean, the distribution for the test is for means:
$\bar{X}$ ~ $N(\mu_X,\frac{\sigma_X}{\sqrt{n}})$
or $t_{df}$
The population parameter is µ.
 If you are testing a single population proportion, the distribution for the test is for proportions or percentages:
P' $N(p,\sqrt{\frac{p \cdot q}{{n}}})$
The population parameter is p.