HTH 320 Exam 2; Ch 6, 7, 8, 9

test statistic

how many standard deviations a sample mean is from the population mean

Inferential Statistics and sampling distributions

Researchers select a sample from a larger population and measure the sample statistic. They then select a sample mean to learn more about the population. when researchers measure sample statistics like mean and variance, they do so to estimate the value of the mean and variance in a population

Standard error of the mean (SEM)

- standard deviation of a sampling distribution - Sampling error - SEM

Four steps to hypothesis testing

- state the hypothesis - set the criteria for a decision - compute the test statistic - make a decision

Factors that decrease standard error

- as the population standard deviation decreases the standard error decreases - sample size increases, the standard error decreases - standard error can increase or decrease based on sample size, and value of the population standard deviation

Sampling distributions: The Mean

Measure a sample mean to estimate the value of the population mean. The sample mean from a randomly selected sample to be equal to the population mean M = U

Sampling strategy: most used in behavioral research

Order doesn't matter, Sample without replacement

Basis for statistical theory

Order matters, sample with replacement

Hypothesis

Systematic way to test claims

Sampling and Conditional Probabilities

a random procedure is used to select a sample from a population (reduces bias) all in the population have an equal chance of being selected so the probability should be the same

Sample distribution

distribution of the mean and variance for all possible samples of a given size from a population

Sampling error

extent to which sample means selected from the same population differ from one another, Difference which occurs by chance is measured by the standard error of mean. Larger values indicates greater sampling error

Variance

gives researchers an idea of how far the value of a sample mean can deviate from the value of the population mean

Sampling with replacement

method of sampling in which each participant selected is replaced before the next selection. This ensures the probability for each selection is the same. Used in development of statistical theory

Sampling without replacement

method of sampling where each participant selected is not replaced before the next selection. Most common method of sampling in behavioral research

Distribution of sample mean follows the central limit theorem

regardless of shape of distribution in a population, the distribution of sample means selected from the population will approach the shape of a normal distribution as the number of samples increases

Central limit theorem

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

Distribution of sample means has minimum variance

sampling distribution of sample means will vary minimally from the value of the population mean

Hypothesis testing

test a hypothesis by determining the likelihood that a sample statistic would be selected if the hypothesis regarding the population parameter were true

Sample mean is an Unbiased estimator

the sample mean we obtain in a randomly selected sample will equal the value of the population mean