Test 2

Identify 3 characteristics of the sampling distribution of the sample mean: calculate the mean and standard error of a sampling distribution of the sample mean and draw the shape of this distribution.

The sample mean has the following 3 characteristics: a. The sample mean is an unbiased estimator. On average, the sample mean we obtain in a randomly selected sample will equal the value of the population mean. b. A distribution of sample means follows the central limit theorem. Regardless of the shape of the distribution in a population, the distribution of sample means selected at random from the population will approach the shape of a normal distribution, as the number of samples in the sampling distribution increases. c. A distribution of sample mean has minimum variance. The sampling distribution of the mean will vary minimally from the value of the population mean. The variance of the sampling distribution of sample means equals the population variance divided by the sample size: The standard error of the mean is the standard deviation of the sampling distribution of the sample means. It is the square root of the variance.

unbiased estimator

any sample statistic obtained from a randomly selected sample that equals the value of its respective population parameter on average.

Explain the relationship between standard error, standard deviation, and sample size.

As the population standard deviation (0) increases, standard error increases. Hence, the father scores in a population deviate from the mean in a population, the farther possible sample means can deviate from the value of the population mean. As the sample size (n) increases, standard error decreases. Hence, the more data you collect, the closer your estimate of the value of the population mean. This relationship is explained by the law of large numbers.

Explain the sample mean is an unbiased estimator of the population mean.

On average, the sample mean obtained in a randomly selected sample will equal the value of the population mean.

standard error

S.E. = t ( √ [(p*q)/n] ) - Pertains to sample (standard deviation of sampling distribution) - S.E. decreases with increasing n b/c you become more confident since you have asked more people (in your sample) - answer to equation is decimal, convert to (+/-) percent error

Distingguish between sampling with replacement and sampling without replacement.

Sampling with replacement is when each participant or item selected is replaced before the next draw. Sampling without replacement is where each item or participant is not replaced before the next draw.

Explain how conditional probabilites are related to sampling without replacement.

Sampling without replacement and conditional probabilities are related in that when we sample without replacement, the probability of each selection is conditional or dependent on the person or item that was selected in the previous selection.

Compare theoretical and experimental sampling strategies.

The theoretical sampling strategy is a sampling method in which we sample with replacement and the order in which a participant is selected matters. Sampling with replacement is a method of sampling in which each participant or item selected is replaced before the next draw. The experimental sampling strategy is a sampling method in which we sample without replacement and the order in which a participant is selected does not matter. Sampling without replacement is a method of sampling in which each participant or item selected is not replaced before the next draw.

Distingquish between sampling where order matters and sampling where order does not matter.

Theoretical sampling stratedgy is the sample used when order matters and experimental sampling strategy is used when order does not matter.

sampling without replacement

a method of sampling in which each participant or item selected is not replaced before the next selection. This method of sampling is the most common method used in behavioral research.

Sample design

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

law of large numbers

a theorem or a rule that increasing the number of observations or the sample size in a study will decrease the standard error. The smaller the standard error, the closer a distribution of the sample means will be to the population mean.

central limit theorem

a theorem that 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.

sampling distribution

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

sampling with replacment

method of sampling in which each participant or item selected is replaced before the next selection. This method of sampling is used in the development of statistical theory.

sampling error

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.

standard error of the mean

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; also stated as standard error.