Chapter 6: Part 2 Flashcards
How can the knowledge of the determination of a z-score be determined?
Probabilities associated with individual sample means can be found, laying the basis for testing hypotheses about sample means
When can the normal distribution be used in place of the binomial distribution?
When there are large numbers of observations
What is a sampling distribution?
Frequency distribution of the complete set of a statistic derived from random samples of a given size drawn from a population
What is a standard normal distribution?
The mean is 0 and the sd is 1
What is the standard normal distribution used to represent?
Real-valued random variable whose distributions are not known
Why is the standard normal distribution useful?
Because any normal distribution can be turned into a standard normal distribution
What does a complete set of values for the sample mean allow us to determine?
probability of particular sample means
What is the symbol for the mean of the distribution of sample means?
Ux(x has a bar)
What is the symbol for the standard deviation of the mean?
o x with a bar
What is the standard error of the mean?
Standard deviation of the sample means
How can you calculate standard error?
the standard deviation (σ) divided by the square root of the sample size (n). It’s written as: SEM = σ/√n
When do you use the standard deviation formula?
When you want to understand the spread of data points in a single sample
When do you use the standard error formula?
Dealing with multiple samples from a population and you want to understand how much the sample means vary
When do you use standard error vs. standard deviation?
standard deviation is used when analyzing individual data points, while standard error is used when analyzing sample means.
What happens when the standard error is smaller?
It is closer to the population mean
What happens if you get a sample mean that is lower than the lowest raw score?
It is not possible
How do you find the mean of means?
taking the determined means adding them up and then dividing them by the frequency numbers
A distribution of sample means gives us ______ possible sample means, and the frequency with which they occur.
all
What is the central limit theorem?
if you have any shape of distribution, and you draw large random samples from the population, then the distribution of the sample means will approach a normal distribution
What does the central limit additionally state?
Mean of the distribution of sample means will be equal to the mean of pop, standard error will be equal to standard deviation of pop / by square root of sample size
What do you need to know to use the central limit theorem?
Mean (u) sd (o) of the pop of scores, and n
What is the first part of the central limit theorem?
Distribution of sample means approaches normal curve as n approaches infinity
What is the second part of the central limit theorem?
Mean of distribution of sample means has same value as mean of pop
What is the third part of the central limit theorem?
Standard error of mean is standard deviation of known pop divided by square root of n
What are the three things that the central limit theorem tells us?
Shape, central tendency, and variability
What happens if the distribution of raw scores is not normally distributed?
Need reasonable sample size to obtain the normal distribution
What is the value that the differences between distribution of sample means and true normal curve are not substantial?
Once sample gets to 30 data points
Will the standard error of the mean always be less than the standard deviation?
Yes
What happens with means of the same population?
More similar than raw values
The mean of a population of IQ scores is 100. What is the mean of the distribution of sample means for samples of size 64?
100
Which formula is appropriate only for use with raw scores?
Z-score (z= (x-u)/o
What is the z-score formula for sample means?
z= (xbar- ubar)/(standard deviation bar)
What is the explanation for the updated z-score formula?
distribution of sample means (μx̄ ) and divide that by the standard error of the mean (σx̄ )
How do you get the area between the z-score and the mean?
subtract the area to the left of our z-score of -1.43 from .5000 (50%) to obtain the area between the z-score and the mean.
When do you use the normal approximation of the binomial?
if it can be assumed to follow a normal distribution
When can you use the normal approximation of the binomial?
the product of the number of trials n and the probability of a success and of a failure on a given trial are both equal to five or more.
Is a binomial distribution discrete?
Yes, consists of successes and failures
What is a discrete variable?
Indivisible no half values
Is the normal distribution continuous?
Yes.
What is a random sampling distribution?
All possible values for any given statistic when we take random samples of same size from pop
What does the sampling distribution represent?
Every possible sample you can take when sampling with replacement
What is the expected value of the sampling distribution?
Mean of sampling will be = to mean of pop
