Chapter 6: Probability

What does the central limit theorem not tell us?

that a variable in a sample is normally distributed

What are the key properties of probability?

1. all outcomes have some probability ranging from 0-1 2. the sum of all possible outcomes must be exactly 1 3. if two outcomes are independent, then the probability of those events occuring is equal to the product of them individually

For the next three questions, consider a variable with the following values for the seven observations in a data set: 35,23,28,37,23,19,31 What is the mode?

23

For the next three questions, consider a variable with the following values for the seven observations in a data set: 35,23,28,37,23,19,31 What is the mean?

28

For the next three questions, consider a variable with the following values for the seven observations in a data set: 35,23,28,37,23,19,31 What is the median?

28

How do you calculate the confidence interval around the mean?

CI = mean plus or minus 1.96(standard error)

Which of the following accurately describes a categorical variable?

Different values mean different things

Which of the folllowing accurately describes an ordinal variable?

Different values mean different things and the categories are ordered from least to greatest

What does it mean by "N becomes large"?

N>100

Which of the following is true for a box-whisker plot?

NOT a box-whisker plot can not be used to display outliers

Which of the following are useful for describing values of a categorical variable?

a bar graph

Which of the following are useful for describing the values of a continuous variable?

a box-whisker plot, a kernal plot, or rank statistics

What is the central limit theorem?

all sampling distributions follow a normal distribution in the limit (ie. they get large in size)

Which of the following accurately describes a continuous variable?

different values mean different things and a one-unit increase in the variable value always means the same thing

How does the central limit theorem work?

for any trait or variable, even those that are not normally distributed in the pop, if repeated size N are drawn from any population, with mean m and standard deviation s, then, as N becomes large, the sampling distribution of sample means will approach normality with mean u and sampling distribution o/n

What is the 65-95-99 rule?

going one standard deviation from the mean in each direction will cover 68% of the data, 2 stand. devs covers 95% and three covers 99%

What is the formula for the standard error?

standard deviation / square root of sample size

What does the Central limit theorem tell us?

the sampling distribution will be normally distributed

What does the standard error tell us?

the uncertainty of the mean without puling hundred of repeated samples

What are parameters?

traits that can be quantified like averages, differences between groups, and relationships among variables