8: Sampling Distributions and z-scores Flashcards
What are probability distributions for discrete variables?
Assigns a probability to each possible value of the variable. Each probability is between 0 and 1. Sum of all probabilites is equal to 1.
What are probability distributions for continuous variables?
Probabilities are assigned to intervals of numbers. Probability for any interval is between 0 and 1. Probability of the interval containing all possible numbers equals 1.
What are parameter values?
The values measures would assume, in the long run, if a randomised experiment or random sample repeatedly took observations on the variable y.
What is the normal distribution?
The most useful and most frequently used distribution. Has familar bell shape. It is even useful when the sample data are not bell shaped. It is characterised by its mean and standard deviation. The probability within any particular standard deviations of the mean is the same for all normal distributions.
What does the probability equal with 1, 2 and 3 standard deviations?
The probability equals 0.68 within 1 standard deviation, 0.95 within 2 standard deviations, 0.997 within 3 standard deviations.
What are z-values?
Normal distribution - for each fixed no. of z, the probability of falling within z standard deviations of the mean depends only on the value of z. The area under the curve between: µ − zσ and µ + zσ. The probability of 0.68 is 1.
What are z-scores?
The z-score for the value of y of a variable is the number of standard deviations that y falls from the mean. z = y - µ / σ
What is a sampling distribution?
A sampling distribution of a statistic is the probability distribution that specifies probabilities for the possible values the statistic can take.
What are examples of statistics?
Sample mean, sample proportion, sample median.
What is the sample mean?
Denoted as y¯. It is a variable, its values varies from sample to sample we draw. Fluctuates around the true mean of the population mean. The mean of the sampling distribution of y¯ equals µ.
What is standard error?
The standard deviation of the sampling distribution of y¯ is called standard error. Denoted as σy¯ .
What is the population distribution?
The distribution from which the sample is selected. It is usually unknown. We can make inferences about is charachteristics - like the parameters µ and σ that describe its centre and spread. The population size is usually denoted as N.
What is the sample data distribution?
The distribution of the data that we actually observe. The sample observations y1, y2, y3…. It can be described by stats - sample mean y¯ and sample standard deivation s. The larger the sample size n, the close the sample stats like y¯ fall to the population parameters such as µ.
What is the sampling distribution of the statistic?
The probability distribution for the possible values of a sample statistic, like y¯. It describes the variability that occurs in the statistic’s value among samples of a certain size.
