Probability

Example of a situation that violates the requirement that probabilities must stay constant from one selection to the next if more than one individual is selected? (2)

1. First draw: p(queen of hearts) = 1/52 2. Second draw: p(queen of hearts) = 1/51 or 0

How do you find the probability corresponding to a particular score (X value)? (2)

1. First transform the score into a z-score 2. Then look up the z-score in the table and read across the row to find the appropriate proportion/probability

How do you find the score (X value) corresponding to a particular proportion? (3)

1. First you look up the proportion in the table 2. Then you read across the row to find the corresponding z-score 3. Then transform the z-score into an X value

We define probability as a ____________ or a ____________

1. Fraction 2. Proportion

Shape of a normal distribution (5)

1. Has a common shape 2. Symmetrical 3. Highest frequency is in the middle 4. Frequencies taper off towards the extremes 5. Has a single mode

The role of probability in inferential statistics? (3)

1. Probability is used to predict what kind of samples are likely to be obtained from a population 2. Thus probability establishes a connection between samples and populations 3. Inferential statistics rely on this connection when they use sample data as a basis for making conclusions about the population

What are the two requirements of Random Sampling?

1. Random sample requires that each individual in the population has an equal chance of being selected 2. Probabilities must stay constant from one selection to the next if more than one individual is selected

A negative z-score means that the tail of the distribution is on the ________ side and the body is on the ___________ side

1. Tail is on the left side 2. Body is on the right side

The proportions of area apply to any normal distribution regardless of (2)

1. The mean 2. The standard deviation

Probability of the body and tail of a z value of +0.25 and a z value of -0.25? (3)

1. They are the same 2. Proportion of the body = 0.5907 3. Proportion of the tail = 0.4013

A positive z-score means that the tail of the distribution is on the ________ side and the body is on the ___________ side

1. right side 2. left side

What is the probability of selecting an ace from a deck of cards?

1/13

What is the probability of selecting the ace of spades in a deck of cards?

1/52

Percentage of area between 1 standard deviation and 2 standard deviations on a normal distribution with z-scores

13.59%

Percentage of area beyond 2 standard deviations on a normal distribution with z-scores

2.28%

Percentage of area between the mean and 1 standard deviation for a normal distribution with z-scores

34.13%

The probability of any specific outcome is determined by

A ratio comparing the frequency of occurrence for that outcome relative to the total number of possible outcomes

What does a random sample requiring each individual in the population to have an equal chance of being selected assure

Assures a lack of bias

Why is probability important

Because it establishes the link between samples and populations

Why can the values in the unit normal table be used to determine probabilities

Because probability is equivalent to proportion

Why do the proportions of the area apply to any normal distribution

Because z-scores define the sections

Specifically what does Column B list in a unit normal table?

Column B lists the proportion in the body of the normal distribution up to the z-score value

Specifically what does Column C list in a unit normal table?

Column C lists the proportion of the normal distribution that is located in the tail of the distribution beyond the z-score value

What does column D list in a unit normal table?

Column D lists the proportion between the mean and the z-score location

For each z score location, what do columns B and C list in the unit normal table

Columns B and C list the proportions in the body and tail, respectively

Column A of the unit normal table

Lists z-score values

You can never have a _______________ even if the corresponding z-score is negative

Negative proportion

What is a score called when it is referred to by its rank?

Percentile

Example of of how relationships between samples and populations are defined in terms of probability

Picking a single marble from a jar of 50 black and 50 white marbles

Relationships between samples and populations are defined in terms of

Probability

What is Probability

Probability is a method for measuring and quantifying the likelihood of obtaining a specific sample from a specific population

Actual research is conducted using a

Sample

Definition of probability

Several different outcomes are possible and the probability of any specific outcome is a fraction or proportion of all possible outcomes

What does the unit normal table list

Several different proportions corresponding to each z-score

What is the percentile rank for a specific X value?

The percentile rank for a specific X value is the percentage of individuals with scores at or below that value

For any known population it is possible to determine

The probability of obtaining any specific sample

What is the percentile rank for a score in a normal distribution?

The proportion to the left of the score

Although a normal distribution can be defined by an equation, it can be described by

The proportions of area contained in each section of the distribution

Because a normal distribution is symmetrical

The proportions on each side of the mean are going to be identical

Because the normal distribution is symmetrical the proportions for the positive and negative values of a specific z-score will be

The same

If the sample has a very low probability of being obtained from a specific population, then

Then it is reasonable for the researcher to conclude that the specific population is probably not the source of the sample

If the sample has a high probability of being obtained from a specific population, then

Then the researcher can conclude that the sample is likely to have come from that population

What do inferential statistics do?

Use sample data to answer questions about the population

Where does research begin?

With a question about an entire population

What are used to identify the sections of a normal distribution

Z-scores

The sections on the left side of a normal distribution have the same _______________ as corresponding sections on the right

area

How is probability expressed

p

Formula of probability

probability of A = number of outcomes classified as A/ total number of possible outcomes