Test 2
inferential statistics
use sample data to draw general conclusions about populations
samples are
variable
Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the expectedvalue for the distribution of sample means? a. 8 b. 80 c. 40 d. 20
B
The standard deviation of the distribution of sample means is called _____. a. the Expected Value of M b. the Standard Error of M c. the sample mean d. the central limit mean
B
A random sample of n = 36 scores is selected from a normal population. Which of the following distributions definitely will be normal? a. The scores in the sample will form a normal distribution. b. The scores in the population will form a normal distribution c. The distribution of sample means will form a normal distribution. d. Neither the sample, the population, nor the distribution of sample means will definitely be normal.
C
A sample of n = 25 scores is selected from a population with μ = 100 with σ = 20. On average, how much error would be expected between the sample mean and the population mean? a. 25 points b. 20 points c. 4 points d. 0.8 points
C
The distribution of sample means (for a specific sample size) consists of _____. a. all the scores contained in the sample b. all the scores contained in the population c. the sample means for all the possible samples (for the specific sample size) d. the mean computed for the specific sample of scores
C
A random sample of n = 4 scores is selected from a population. Which of the following distributions definitely will be normal? a. The scores in the sample will form a normal distribution. b. The scores in the population will form a normal distribution c. The distribution of sample means will form a normal distribution. d. Neither the sample, the population, nor the distribution of sample means will definitely be normal.
D
The Standard Error of M provides a measure of _____. a. the maximum possible discrepancy between M and µ b. the minimum possible discrepancy between M and µ c. the exact amount of discrepancy between each specific M and µ d. None of the other 3 choices is correct.
D
a. is always normal b. is normal only if the population distribution is normal c. is normal only if the sample size is greater than 30 d. None of the other 3 choices is correct. Both b and c have to be true for the distribution of sample means to be approximately normal
D
primary use of the distribution of sample means
is to find the probability associated with any specific sample
magnitude of standard error
law of large numbers and population variance
sample means
mean= M std. dev.= osymbol subscript m
Sample
mean= m std. dev= s
Population
mean= u symbol std. dev= o symbol
variability of scores
measured by the standard deviation
sampling error
natural discrepancy, or the amount of error, between a sample statistic and its corresponding population parameter
distribution of sample means
o subscript m= o/squareroot of n
standard error
the variability of sample error
as the sample size increases...
there is less error between the sample and the mean
sampling error
there will be discrepancy between a sample mean and the true population mean
as sample size increases, the value of the standard error decreases.
true
Central limit theorem
u symbol subscript m= mean of the sample means is always equal to u.
M is an
unbiased statistic
central limit theorem: shape of the distribution of normal if...
1. the population is normal or 2. sample size is 30 or more
The mean of the distribution of sample means is called _____. a. the Expected Value of M b. the Standard Error of M c. the sample mean d. the central limit mean
A
The symbol that corresponds to the Standard Error of M is _____. a. σM b. µ c. σ
A
When a random sample is selected from a population, the sample mean is not expected to be exactly equal to the population mean. On average, the size of the difference between a sample mean and the population mean is predicted by _____. a. the Standard Error b. the expected value c. the mean of the population d. the standard deviation of the population
A
distribution of sample means
a collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population.
error
a difference that is due to chance
numerical value of z-score indicates...
distance between M and u measured in terms of Standard Error.
the distribution of sample means is always normal shaped.
false
a distribution of statistics is obtained by
selecting all the possible samples of a specific size (n) from a population
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.
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.
z-score represents
the location of a score in a sample or in a population
distribution of sample means and z-scores
z=M-u/o subscript m
