Week 4 Chapter 6 Flashcards
probability
fraction or proportion of all the possible outcomes. If the possible outcomes are identified as A, B, C, D, and so on, then probability of A = number of outcomes classified as A / total number of possible outcomes
random sampling
selection process wherein each individual in the population has an equal chance of being selected
simple random sample
data set obtained using selection process wherein each individual has equal chance of being selected
independent random sample
data set obtained using selection process wherein the probability of being selected stays constant
independent random sampling
selection process wherein the probability of being selected stays constant from one selection to next
sampling with replacement
selection process that returns individuals to the population in order to keep probabilities from changing
sampling without replacement
selection process that does not require constant probabilities
unit normal table
list of proportions of the normal distribution for a full range of possible z-score values
percentile rank
portion of individuals in a distribution with scores less than/equal to the specific score
percentile
score referred to by its portion of scores less than/equal to the specific score
the role of inferential statistics is to use the sample data as the basis for answering questions about the population. To accomplish this goal, inferential procedures are typically built around the concept of
probability. Specifically, the relationships between samples and populations are usually defined in terms of probability.
By knowing the makeup of a population, we can determine the probability of obtaining specific samples. In this way, probability gives us a connection between populations and samples, and this connection is
the foundation for the inferential statistics
the goal of inferential statistics is to begin with
a sample and then answer a general question about the population. We reach this goal in a two-stage process. In the first stage, we develop probability as a bridge from populations to samples. This stage involves identifying the types of samples that probably would be obtained from a specific population. Once this bridge is established, we simply reverse the probability rules to allow us to move from samples to populations
all the possible probability values are contained in a limited range. At one extreme, when an event never occurs, the probability is zero, or 0%. At the other extreme, when an event always occurs, the probability is
1, or 100%. Thus, all probability values are contained in a range from 0 to 1. For example, suppose that you have a jar containing 10 white marbles. The probability of randomly selecting a black marble is p(black) = 0/10 = 0. The probability of randomly selecting a white marble is p(white) = 10/10 = 1
For the preceding definition of probability to be accurate, it is necessary that the outcomes be obtained by a process called random sampling.
A second requirement, necessary for many statistical formulas, states that if more than one individual is being selected, the probabilities must stay constant from one selection to the next. Adding this second requirement produces what is called independent random sampling. The term independent refers to the fact that the probability of selecting any particular individual is independent of the individuals already selected for the sample. For example, the probability that you will be selected is constant and does not change even when other individuals are selected before you are.
independent random samples
Independent random sampling requires that each individual has an equal chance of being selected and that the probability of being selected stays constant from one selection to the next if more than one individual is selected. A sample obtained with this technique is called an independent random sample or simply a random sample.
To keep the probabilities from changing from one selection to the next, it is necessary to
return each individual to the population before you make the next selection. This process is called sampling with replacement. The second requirement for random samples (constant probability) demands that you sample with replacement.
Random sampling requires sampling with replacement. What is the goal of sampling with replacement?
It ensures that the probabilities stay constant from one selection to the next.
a distribution is normal if and only if it has all the
right proportions.
In the unit normal table, the first column (A) lists z-score values corresponding to different positions in a normal distribution. If you imagine a vertical line drawn through a normal distribution, then the exact location of the line can be described by one of the z-score values listed in column A. You should also realize that a vertical line separates the distribution into two sections: a larger section called the body and a smaller section called the tail. Columns B and C in the table identify
the proportion of the distribution in each of the two sections. Column B presents the proportion in the body (the larger portion), and column C presents the proportion in the tail. Finally, we have added a fourth column, column D, which identifies the proportion of the distribution that is located between the mean and the z-score.
When using the unit normal table, for a negative z-score, the tail of the distribution is on the left side and the body is on the right. For a positive z-score,
the positions are reversed. However, the proportions in each section are exactly the same in the body and in the tail.
the unit normal table does not list negative z-score values. To find proportions for negative z-scores, you must look up the corresponding proportions for the
positive value of z
In the unit normal table, Although the z-score values change signs (+ and −) from one side to the other, the proportions are always
positive. Thus, column C in the table always lists the proportion in the tail whether it is the right-hand tail or the left-hand tail.
The unit normal table can be used only with normal-shaped distributions. If a distribution is not normal, transforming X values to z-scores will
not make it normal
to answer probability questions about scores (X values) from a normal distribution, you must use the following two-step procedure
- Transform the X values into z-scores.
2. Use the unit normal table to look up the proportions corresponding to the z-score values.
