PSY 250 Exam 2 Chapters 5 - Part of 7

FYI (37)

The one-sample z test used to test hypotheses about a population mean when the population variance is known (37)

FYI (25)

The sample mean is an unbiased estimator of the value of the population mean (25)

One-sample z test

Is a statistical procedure used to test hypotheses concerning the mean in a single population with a known variance

Random Event

Is any event in which the outcome observed can vary

Fixed Event

Is any event in which the outcome observed is always the same

Sampling Error

Is the extent to which sample means selected from the same population differ from one another. This difference, which occurs by chance, is measured by the standard error of the mean

P Value

Is the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true. The p value for obtaining a sample outcome is compared to the level of significance or criterion for making a decision

Rejection region

Is the region beyond a critical value in a hypothesis test. When the value of a test statistic is in the rejection region, we decide to reject the null hypothesis; otherwise, we retain the null hypothesis

Standard error of the mean or standard error

Is the standard deviation of a sampling distribution of sample means. It is the standard error or distance that sample mean values deviate from the value of the population mean

Obtained value

Is the value of a test statistic. This value is compared to the critical value(s) of a hypothesis test to make a decision. When the obtained value exceeds a critical value, we decide to reject the null hypothesis; otherwise, we retain the null hypothesis

z score

The numerical value of a z score specifies the distance or the number of standard deviations that a value is above or below the mean

FYI (27)

The standard error of the mean is the standard deviation of the sampling distribution of sample means (27)

FYI (11)

The standard normal distribution is one of the infinite normal distributions - it has a mean of 0 and standard deviation of 1 (11)

FYI (7)

In a normal distribution, 50% of all data fall above the mean, the media, and the mode, and 50% fall below these measures. (7)

FYI (8)

In a normal distribution, the mean can equal any value between positive infinity and negative infinity; the standard deviation can equal any positive value greater than 0

FYI (2)

Probability allows us to make predictions regarding random events (2)

FYI (36)

Researchers make decisions regarding the null hypothesis. The decision can be to retain the null (p>.05) or reject the null (p<_.05) (36)

FYI (21)

Researchers measure a mean and variance in a sample to gauge the value of the mean and variance in a population (21)

Sample Space

Is the total number of possible outcomes that can occur in a given random event

FYI (5)

The behavioral data that researchers measure often tend to approximate a normal distribution (5)

Probability

(symbolized as p) is the frequency of times an outcome occurs divided by the total number of possible outcomes

FYI (40)

A critical value marks the cutoff for the rejection region (40)

Critical value

A cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means result in a decision to reject the null hypothesis

FYI (42)

A nondirectional test is conducted when it is impossible or highly unlikely that a sample mean will fall in the direction opposite to that stated in the alternative hypothesis (42)

Unit Normal Table or z table

A type of probability distribution table displaying a list of z scores and the corresponding probabilities (or proportions of area) associated with each z score listed

The Normal Distribution

Also called the symmetrical, Gaussian, or bell-shaped distribution, is a theoretical distribution in which scores are symmetrically distributed above and below the mean, the median, and the mode at the center of the distribution

z statistic

An inferential statistic used to determine the number of standard deviations in a standard normal distribution that a sample mean deviates from the population mean stated in the null hypothesis

Directional test or one-tailed tests

Are hypothesis test in which the alternative hypothesis is stated as greater than (>) or less than (<) a value stated in the null hypothesis. Hence, the researcher is interested in a specific alternative to the null hypothesis.

FYI (17)

Because the normal distribution is symmetrical, probabilities associated with positive z scores are the same for corresponding negative z scores (17)

Significance or statistical significance

Describes a decision made concerning a value stated in the null hypothesis. When the null hypothesis is rejected we reach significance. When the null hypothesis is retained, we fail to reach significance

Nondirectional tests or two tailed tests

Hypothesis test in which the alternative hypothesis is stated as not equal to a value stated in the null hypothesis. Hence, the researcher is interested in any alternative to the null hypothesis

FYI (32)

Hypothesis testing is a method of testing whether hypotheses about a population parameter are likely to be true (32)

FYI (14)

For normally distributed data, we use the unit normal table to find the probability of obtaining an outcome in relation to all other outcomes (14)

Sampling Distribution

For the mean is a distribution of all sample means that could be obtained in samples of a given size from the same population

FYI (39)

For two-tailed tests, the alpha is split in half and placed in each tail of a standard normal distribution (39)

FYI (34)

In behavioral science, the criterion or level of significance is typically set at 5%. When the probability of obtaining a sample mean would be less than 5% if the null hypothesis were true, then we reject the value stated in the null hypothesis (34)

FYI (24)

In experimental sampling, the order of selecting individuals does not matter, and each individual selected is not replaced before selecting again (24)

FYI (33)

In hypothesis testing, we conduct a study to test whether the null hypothesis is likely to be true (33)

Sample Design

Is a specific plan or protocol for how individuals will be selected or sampled from a population of interest

Hypothesis

Is a statement or proposed explanation for an observation, a phenomenon or scientific problem that can be tested using the research method. A hypothesis is often a statement about the value for a parameter in the population

FYI (16)

In the standard normal distribution, z scores above the mean are positive; z scores below the mean are negative (16)

FYI (23)

In theoretical sampling, in order of selecting individuals matters, and each individuals selected is replaced before sampling again (23)

Alternative Hypothesis (H1)

Is a statement that directly contradicts a null hypothesis by stating that the actual value of a population parameter is less than, greater than, or not equal to the value state in the null hypothesis.

Level of significance or significance level

Is a criterion of judgment upon which a decision is made regarding the value stated in a null hypothesis. The criterion is based on the probability of obtaining a statistic measured in a sample if the value stated in the null hypothesis were true.

The Standard Normal Transformation or z transformation

Is a formula used to convert any normal distribution with any mean and any variance to a standard normal distribution with a mean equal to 0 and a standard deviation equal to 1

Test Statistic

Is a mathematical formula that identifies how far or how many standard deviations a sample outcome is from the value stated in a null hypothesis. It allows researchers to determine the likelihood of obtaining sample outcomes if the null hypothesis were true. The value of the test statistic is used to make a decision regarding a null hypothesis.

Hypothesis testing or significance testing

Is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. In this method, we test a hypothesis by determining the likelihood about a sample statistic would be selected if the hypothesis regarding the population parameter were true

Sampling without Replacement

Is a method of sampling in which each participant or item selected is nor replaced before the next selection. This method of sampling is the most common method used in behavioral research

Sampling with Replacement

Is a method of sampling in which each participant or item selected is replaced before the next selection. Replacing before the next selection ensures that the probability for each selection is the same. This method of sampling is used in the development of statistical theory.

The Standard Normal Distribution or z distribution

Is a normal distribution with a mean equal to 0 and a standard deviation equal to 1. The standard normal distribution is distributed in z score units along the x-axis.

FYI (9)

Proportions of area under a normal curve are used to determine the probabilities for normally distributed data (9)

FYI (6)

Most behavioral data approximate a normal distribution. Rarely are behavioral data exactly normally distributed. (6)

FYI (38)

Nondirectional tests are used to test hypotheses when we are interested in any alternative to the null hypothesis (38)

FYI (1)

Probability is a measure for the likelihood of observing an outcome in a random event. (1)

FYI (4)

Probability varies between 0 and 1 and is never negative. Hence, a specified outcome is either probable (0 < p <-1) or improbable (p=0) (4)

FYI (22)

Sampling without replacement means that the probability of each selection is conditional. The probabilities of each selection are not the same. (22)

Null hypothesis (H0)

Stated as the null, is a statement about a population mean, that is assumed to be true, and a hypothesis test is structured to decide whether or not to reject this assumption

Law of large numbers

States that increasing the number of observations or samples in a study will decrease the standard error. Hence, larger samples are associated with closer estimates of the population mean on average

FYI (26)

The central limit theorem explains that the shape of a sampling distribution of sample means tends toward a normal distribution, regardless of the distribution in the population (26)

FYI (29)

The larger the standard deviation in the population, the larger the standard error (29)

FYI (30)

The law of large numbers explains that the larger the sample size, the smaller the standard error (30)

FYI (13)

The mean in any normal distribution corresponds to a z score equal to 0 (13)

FYI (10)

The tails of a normal distribution never touch the x-axis, so it is possible to observe outliers in a data set that is normally distributed (10)

FYI (15)

The total area is .5000 above the mean and .5000 below the mean in a normal distribution (15)

FYI (20)

The unit normal table allows us to locate raw scores, x, and determine probabilities, p, for data that are normally distributed (20)

FYI (19)

The unit normal table can be used to locate a cutoff score for a given proportion for data that are normally distributed (19)

FYI (18)

The unit normal table can be used to locate scores that fall within a given proportion or percentile (18)

FYI (41)

The z statistic measures the number of standard deviations, or z scores that a sample mean falls above or below the population mean stated in the null hypothesis (41)

FYI (12)

The z transformation formula converts any normal distribution to the standard normal distribution with a mean equal to 0 and standard deviation equal to 1 (12)

FYI (31)

The z transformation is used to determine the likelihood of measuring a particular sample mean, from a population with a given mean and variance (31)

FYI (28)

To compute the standard error of the mean, divide the population standard deviation by the square root of the sample size (28)

FYI (35)

We use the value of the test statistic to makes a decision regarding the null hypothesis (35)

Central Limit Theorem

explains that regardless of the distribution of scores in a population, the sampling distribution of sample means selected at random from that population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases