Randomness and Probablility

Question 1

What defines a random phenomenon?

Answer 1

A phenomenon is random if the individual outcomes of a single repitition are uncertain.

Question 2

What is the probability of an outcome?

Answer 2

The probability of any outcome is the proportion of times it would occur in a large number of repition.

Question 3

What is the law of large numnbers?

Answer 3

As the sample size increases, the sample mean gets closer to the population or theoretical mean, and the sample proportion gets closer to the population or theoretical proportion.
or
as the sample gets bigger, it gets closer and closer to the population value.

Question 4

What is an event?

Answer 4

An event is a set of outcomes of a random phenomenon typically denoted by A, B etc.
The probability of an event A is written P(A)

Question 5

What is probability fact 1

Answer 5

A probability is a number between 0 and 1 (or between 0% and 100%)

Question 6

What is probability fact 2?

Answer 6

Something has to happen, and all possible outcomes must = 1.

Question 7

What is probability fact 3?

Answer 7

The probability an event does not occur is: P(notA) = 1 - P(A)
The event will or will not happen and the two options add up to 1. These are complementary events.

Question 8

What is Probability fact 4?

Answer 8

If two events have no outcomes in common, the probability one or the other (or both) occurs is the sum of their individual probabilities.

Question 9

What is probability fact 5?

Answer 9

This is the multiplication rule. For two independent events A and B, the probability both occur together is P(A and B) = P(A) x P(B).
Independent events: If one event occurs it has no effect on whether the other one occurs or not.

Question 10

What are random variables?

Answer 10

Any variable taking on numeric values is called a random variable. Quantitative variables are obviously random variables: they take on numeric values.

Question 11

How can a categorical variable become a random variable?

Answer 11

If we assign numbers to the categorical variables.

Question 12

What is a discrete variable?

Answer 12

Discrete random variables take values that can be individually listed.

Question 13

What are continuous random variables?

Answer 13

Continuous random variables can have fractional values. For example heights of adults can have a fraction.

Question 14

What is a probability model?

Answer 14

A probability model is:

1. a description or display of the values of a random variable and the probabilities of taking those values.
2. a theoretical idea
3. is often used to model data and provide a useful approximation to reality.

Question 15

What is statistical inference?

Answer 15

When we use a sample to make an estimate of the population.

Question 16

What is a confidence interval?

Answer 16

When you want to estimate a population parameter. That is when you want an interval estimate.

Question 17

What is hypothesis testing?

Answer 17

When you use a sample data to examine if there is evidence to support a theory about a population.

Question 18

What is essential when hypothosis testing?

Answer 18

You must state what you are trying to prove before you collect the data.

Question 19

What question does Hypothesis testing answer?

Answer 19

Does the data support our assumption, or is it evidence against the assumption?

Question 20

What are the 4 steps of hypothesis testing?

Answer 20

1. State the null and alternative hypotheses.
2. Check all relevant assumptions have been met.
3. Assume the null hypothesis is true and calculate the value of the test statistic.
4. Determine the P-value, a measure of the plausibility of the null hypothesis.
5. Conclusion in context.

Question 21

What are the two types of hypothesis test?

Answer 21

1. Research hypothesis.

2. Manufacturer’s claims.