Statistics Ch.6 Clarifying the concepts
Why does the standard error become smaller by increasing the sample size?
It becomes smaller because it's calculated by dividing the standard deviation of the population of individual scores by the square root of the sample size, N. Thus, as sample size increases, the denominator increases, and the standard error becomes ever smaller.
What are the mean and standard deviation of the z distribution
The mean is 0 and the standard deviation is 1.
Give three reasons why z scores are useful
z scores are useful because 1) they give us a sense of where a score falls in relation to the mean of its population (in terms of standard deviation of its population), 2) they allow us to compare scores from different distributions, and 3) they can be transformed into percentiles.
What does a z statistic - a z score based on a distribution of means - tell us about a sample mean?
The z statistic tells us how many standard errors a sample mean is from the population mean.
What does the symbol Um stand for?
The symbol μ_M stands for the mean of the distribution of means. The µ indicates that it is the mean of a population, and the subscript M indicates that the population is composed of sample means - the means of all possible samples of a given size from a particular population of individual scores.
What is a z score
A z score is a way to standardize data; it expresses how far a data point is from the mean of its distribution in terms of standard deviation.
Why is the central limit theorem such an important idea for dealing with a population that is not normally distributed ?
The central limit theorem asserts that repeated sampling of means will shift a severely skewed distribution of a population's scores toward a normal distribution of means and, thus, toward a normal curve.
How does the size of a sample of scores affect the distribution of data?
The distribution of sample scores approaches normal as the sample size increases, assuming the population is normally distributed.
What point on the normal curve represents the most commonly occuring observation?
The highest point on the curve, or the center of the normal curve, represents the most commonly occurring observation.
Explain how the word standardize is used in everyday conversation, then how staticians use it
People sometimes use the word standardize to refer to making everything the same. Statisticians use the word to refer to situations in which they transform raw scores from different scales and put them all on the same scale, often on the z distribution.
Explain how the word normal is used in everyday conversation and how statisticians use it
In everyday conversation, the word normal is used to refer to events or objects that are common or typically occur. Statisticians use the word to refer to distributions that conform to a specific bell-shaped curve, with a peak in the middle where most of the observations lie, and symmetric areas underneath the curve on either side of the midpoint. This normal curve represents the pattern of occurrence of many different kinds of events.
Each of the following equations has an error. Identify it
a) This is the formula for standard error, except that you need to replace the µ with σ. b) This is the formula for the z statistic, except that you need to replace the µ with M. c) This is the formula for the z statistic, except that you need to replace the σ with σ_M. d) This is the formula for a z score, except that you need to replace the σ_M with σ.
