Probability Rules and Properties
This rule is used when calculating the probability of all outcomes that are NOT Event A.
P(not A) = 1 - P(A)
What is the Complement Rule
The number of objects that are free to vary;
n-1
What is Degrees of Freedom
The probability that an event will occur assuming that the null hypothesis is true.
"If the p is lo, the ho must go"
What is the p-value
H_0: mu = 255
H_1: mu < 255
What type of tailed test is this?
What is a left-tailed test
Variables can be categorized into two types of data, ___________ and ____________
*Hint: They both start with a Q!
What is Qualitative and Quantitative
This rule is used when trying to calculate the probability of the occurence of event A OR event B
* If the events are mutually exclusive...
P(A or B) = P(A) + P(B)
* If the events are NOT mutually exclusive...
P(A or B) = P(A) + P(B) - P(A and B)
What is the Addition Rule
A range of numbers that estimates/captures the value of an unknown population parameter.
point estimate ± margin of error
______ < p (or )< ________
( _____ , ______ )
What is Confidence Interval
The statement that is assumed to be true about the population (aka the baseline)
What is the null hypothesis
If p = 0.2 and
alpha = 0.05,
then do we Reject of Fail to Reject the null hypothesis?
Fail to Reject
These symbols represent what type of statistics?
p and hat p
Proportions
Sample:
hat p
Population:
p
This rule is used when trying to calculate the probability of the occurence of both events A AND B.
* If the events are independent...
P(A and B) = P(A) * P(B)
* If the events are dependent...
P(A and B) = P(A) * P(B|A)
* If the events are mutually exclusive...
P(A and B) = 0
What is the Multiplication Rule
the percent expression of the probability that the confidence interval will contain the true population parameter
Examples: 90%, 95%, 99%
What is Confidence Level
The probabilility that a Type 1 error will occur; we compare the p-value to this number in order to determine if we Reject or Fail to Reject the null hypothesis
What is alpha or the Significance Level
Find the
t_(alpha/2,df)
value for a normally distributed population when n=15 and with a confidence level of 99%
What is 2.977
During an experiment, this variable is known as the independent variable. It is the variable that is controlled or manipulated.
What is the explanatory variable?
If the occurrence of one event directly affects the occurence of another event, these events are known as...
What are Dependent Events
A sample statistic that is used to estimate the corresponding population parameter
Examples:
hat p, bar x
What is the point estimate
Occurs when you reject the null hypothesis when it was in fact true (aka False Positive)
Type 1 Error
Convert the Confidence Interval for p, 54.6 ± 13.7, into a tri-linear inequality and into interval notation,
40.9 < p < 68.3
(40.9 , 68.3)
During an experiment, this variable is known as the dependent variable. It is the variable that is measured, counted or observed.
What is the response variable?
If the occurrence of one event has no effect on the probability of another event occuring, these events are known as...
What are Independent Events
t_(critical) * s/sqrtn
OR
z_(critical) * sqrt((p(1-p))/n)
What is the Margin of Error
Occurs when you fail to reject the null hypothesis when it is in fact false (aka False Positive)
Type 2 Error
What are the null and alternative hypthoses if we want to test the claim that the proportion of people who own cats is smaller than 40% at a 0.01 significance level?
H_0: p = 0.4
H_1: p <0.4
In order to form a box plot, you need to know the statistics that make up the 5 Number Summary. These 5 Summary Statistics are known as...
What is the Minimum, Q1, the Median = Q2, Q3, and the Maximum?