Chapter 7 Probability and Samples

Inferential statistics

uses sample data to draw general conclusions about populations

A. True The sample size is in the denominator of the equation

As sample size increases, the value of the standard error decreases. A. true B. false

has a mean M and a s.d. S

Distribution of a sample from the original scores:

has a mean µ and a s.d. σ

Distribution of the original population of scores:

has a M=µ and a σM=σ/√n

Distribution of the sample means taken from each possible random saple in a given population size:

C. M=88 for a sample of n=25

For a normal population with a mean of 80 and a standard deviation of 20, which of the following samples is least likely to be obtained? A. M=88 for a sample of n=4 B. M=84 for a sample of n=4 C. M=88 for a sample of n=25 D. M=84 for a sample of n=25

B. M=90 for a sample of n=25 scores

For a sample selected from a normal population with mean of 100 and standard deviation of 15, which of the following would be the most extreme and unrepresentative? A. M=90 for a sample of n=9 scores B. M=90 for a sample of n=25 scores C. M=95 for a sample of n=9 scores D. M=95 for a sample of n=25 scores

sample means that are farther away from the population mean and sample size will be larger

For samples that are least likely to be obtained you will look for--

the mean that will be farther from the population mean and the sample size will be larger

For samples that are the most extreme and unrepresentative you will look for-

the population from which the samples are selcected is normal or the number of scores is >30

The distribution of sample means is almost perfectly normal in either of two conditions:

B. False It is normal shaped if the population is normal or n>30

The distribution of sample means is always normal shaped A. true B. flase

normal in shape

The distribution of sample means is approximately

population variance

The greater the variance in the population, the less probable it is that the sample mean will be close to the population mean.

the less variability-you betta off

The larger the sample error-

A. false Individual samples will vary from the population mean

The mean of the sample is always equal to the population mean. A. false B. true

any particular sample

The primary use of the distribution of sample means is to find the probability associated with

difference is expected on average between sample and population means

The standard of error of the mean tell us how much

M that is close to the population mean and a sample size that is smaller

To find samples that occur most often in a distribution you will look for a

Central Limit Theorem

applies to any population with mean and standard deviation distribution of sample means will approach normal as the amount increases distribution of sample means will always have the same mean of populations standard deviation will always be equal to sigma/square root of n

Mean of distribution of sample means or the expected value of M

is equal to the mean of the population of scores, "mu"

a distribution of sample means

is the collection of sample means for all of the possible random samples of a particular size (n) that can be obtained from a population

Standard deviation

is the distance between a score and the population mean -it is used when working with a distribution of scores

standard error

the standard deviation of the sample scaores noted as "sigma"M

B. Neither the sample, the population, nor the distribution of sample means will definitely be normal.

A random sample of n = 4 scores is selected from a population. Which of the following distributions definitely will be normal? Select one: a. The distribution of sample means will form a normal distribution. b. Neither the sample, the population, nor the distribution of sample means will definitely be normal. c. The scores in the sample will form a normal distribution. d. The scores in the population will form a normal distribution

A. A sample of n=25 scores with M=102

A sample is obtained from a population with a mean of 100 and a standard deviation of 20. Which of the following samples would produce the z-score closest to zero? A. A sample of n=25 scores with M=102 B. A sample of n=100 scores with M=102 C. A sample of n-25 scores with M=104 D. A sample of n=100 with M=104

A. false A z-score of 3.00 is an extreme, or unlikely z-score

A sample mean with z=3.00 is a fairly typical, representative sample A. false B. true

changes an original distribution into a normal distribution

A sampling distribution of all the means of all possible samples

A. The sample means tend to form a normal-shaped distribution.

If all the possible random samples of size n=25 are selected from a population with mean of 80 and standard deviation of 10 and the mean is computed for each sample, then what shape is expected for the distribution of sample means? A. The sample means tend to form a normal-shaped distribution. B. The distribution of sample means will have the same shape as the sample distribution. C. The sample will be distributed evenly across the scale, forming a rectangular-shaped distribution D. There are thousands of possible samples and it is impossible to predict the shape of the distribution.

D. 80

If random samples, each with n=4 scores, are selected from a normal population with mean of 80 and a standard deviation, then what is the expected value of the mean for the distribution of sample means? A. 2.5 B. 5 C. 40 D. 80

sample means differ from each other

If we take more than one sample from a population the samples differ from each other and the

C. 80

Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the expected value for the distribution of sample means? Select one: a. 8 b. 20 c. 80 d. 40

1- calculate the standard error 2- calculate the z-score of sample means 3- use the unit normal table to find probability

Steps in calculating probability from a population:

B. It stays constant

What happens to the expected value of M as sample size increases? Select one: a. It decreases b. It stays constant c. It also increases

C. It decreases

What happens to the standard error of M as sample size increases? Select one: a. It stays constant b. It also increases c. It decreases

D. the expected value of M

What term is used to identify the mean of the distribution of sample means? Select one: a. the sample mean b. the standard error of M c. the central limit mean d. the expected value of M

means and standard error of means

When reporting results of experiments scientists provide

C. Increasing the sample size and decreasing the standard deviation

Which of the following would cause the standard error of M to get smaller? A. Increasing both the sample size and the standard deviation B. Decreasing both the sample size and standard deviation C. Increasing the sample size and decreasing the standard deviation D. Decreasing the sample size and increasing the standard deviation

z= M-µ/σM

Z-score formula for the sample of means=

Standard error

the distance between a sample mean and the population mean -it is the mean of sample taken from a population

Law of large numbers

the larger the sample size, the more probable it is that the sample mean will be close to the population mean

sampling error

the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter

for the expected value of the mean

with "expected value of" the question is asking?