Recap Statistics 2

Question 1

Inferential statistics

Answer 1

drawing conclusions or inferences about populations based on sample data (statistical inference)

Question 2

What is a parameter?

Answer 2

It is a measure of a characteristic of an entire population (a mass of all units under consideration that share common characteristics) based on all the elements within that population. For example, all people living in one city, all-male teenagers in the world, all elements in a shopping trolley, or all students in a classroom.

Question 3

What is a statistic?

Answer 3

It’s a measure of characteristic saying something about a fraction (a sample) of the population under study. A sample in statistics is a part or portion of a population. The goal is to estimate a certain population parameter.

Question 4

notation of population parameter

Answer 4

In population parameter, population proportion is represented by P, mean is represented by µ (Greek letter mu), σ2 represents variance, N represents population size, σ (Greek letter sigma) represents standard deviation, σx̄ represents Standard error of mean, σ/µ represents Coefficient of variation, (X-µ)/σ represents standardized variate (z), and σp represents standard error of proportion.

Question 5

notation sample statistic

Answer 5

In sample statistics, mean is represented by x̄ (x-bar), sample proportion is represented by p̂ (p-hat), s represents standard deviation, s2 represents variance, sample size is represented by n, sx̄ represents Standard error of mean, sp represents standard error of proportion, s/(x̄) represents Coefficient of variation, and (x-x̄)/s represents standardized variate (z).

Question 6

Probability theory

Answer 6

Probability theory, a branch of mathematics concerned with the analysis of random phenomena. The outcome of a random event cannot be determined before it occurs, but it may be any one of several possible outcomes. The actual outcome is considered to be determined by chance.

• -> the mathematical tool for making inference from a sample to a population in statistics
• -> describes the probability distribution of a random variable; first step to make inference about the population

Question 7

random variable

Answer 7

A random variable is a numerical description of the outcome of a statistical experiment (random process)

• a statistic based on a sample is treated as a random variable
• written in upper case letter X,Y

Question 8

Example of a random variable

Answer 8

• the height of a randomly chosen Dutch male

Question 9

Discrete random variable

Answer 9

values are countable

Discrete Random Variables. … A discrete variable is a variable which can only take a countable number of values. In this example, the number of heads can only take 4 values (0, 1, 2, 3) and so the variable is discrete. The variable is said to be random if the sum of the probabilities is one.

Question 10

continuous random variable

Answer 10

values are uncountable

180.1,180.01…

Question 11

Probability distribution

Answer 11

a function or rule that assigns a probability to each possible value in the sample space
P(X=x), or simply P(x)

Question 12

Example of a discrete probability distribution

Answer 12

Binomial

Question 13

Binomial Distribution

Answer 13

• n independent trails
• each trial with success rate p (failure rate 1-p)
• the # of successes among n trails is a binomial random variable with binomial distribution

Question 14

What is special about continuous probability distribution?

Answer 14

• impossible to list all values
• zero probability associated with each single value
• -> focus on the probabilities for a range of values: P(a

Question 15

What is a continuous probability distribution?defined?

Answer 15

by a probability density function (PDF)

Question 16

What happens if you increase the mean of a normal distribution?

Answer 16

The curve shifts to the right

Question 17

What happens if you increase the SD of a normal distribution?

Answer 17

The curve flattens. (Variation increases, you find more values far away from the mean and less near the mean)

Question 18

What is a standard normal distribution?

Answer 18

The standard normal distribution is a special case of the normal distribution . It is the distribution that occurs when a normal random variable has a mean of zero and a standard deviation of one. The normal random variable of a standard normal distribution is called a standard score or a z score.

Z=(X-u)/SD

Question 19

Cumulative probability distribution (CDF)

Answer 19

• defines the probability that a random variable X is less than or equal to a value x

A cumulative probability refers to the probability that the value of a random variable falls within a specified range. Frequently, cumulative probabilities refer to the probability that a random variable is less than or equal to a specified value.

Question 20

Example continuous probability distribution

Answer 20

The Normal distribution

Question 21

Probability density function properties

Answer 21

• f(x) is defined over a range (a, b)
• f(x) >0, for all x btw. a and b
• the total area under the curve btw. a and b is 1