Business Statistics

Central Limit Theorem (CLT): If the sample size is more than 30, the shape of the sampling distribution of the sample mean is close to a normal probability distribution.

Conditions of sample
mean to be normal

Distribution unknown, n≥30

Normal distribution
(regardless of sample size)

Point Estimate (PE):
Uses one value for estimation

sample mean is the PE of
population mean

's' is the PE of population
standard deviation

Interval Estimate:
Uses intervals for estimation

Conditions

Population Normal?

No

Is n≥30?

Yes(CLT)

Use z-distribution

Yes

Is σ known?

No, Is n≥30?

No, Use t-distribution

Yes (CLT), Use z-distribution

Yes, use z-distribution

hypothesis: statement or assumption

5 Steps
1. State null and alternate hypothesis
2. State level of significance
3. Identify test distribuition and calculate Test Statistic
4. Make a Decision Rule
5. Make a decision
- Reject null, accept alternate
- Do not reject null

Hypothesis Testing:
Right-tailed, Left-tailed, Two-tailed

Characteristics:
1. x2 values are non-negative
2. postively skewed
3. when degree of freedom changes, new distribution

Types of Testing
1. Goodness-of-Fit Test

H0: There is no difference between fo and fe
H1: There is a difference between fo and fe

Test Statistics: x2 =∑[(f_o-f_e )^2/f_e ]

Normal Distribution:
Mean = Median = Mode

Characterisitcs of Normal Distribution
1. σ = 1, μ=0
2. Disitribuition is symmetrical
3. Area under curve = probability
4. Area under curve = 1

Finding z-value
z=(x-µ)/σ

Finding z-v

Terms: Experiment, Outcome,
Sample Space, Event

Rules

1. Complement Rule
2. General Addition Rule
- Intersection of 2 events
- Union of 2 events
- General Addition Rule
- Mutually Exclusive Events
3. Conditional Probability
4. Multiplication Rule

Correlation Analysis

Coefficient of
Correlation (r)

Negative, Positive,
or No correlation

Coefficient of
Determination (r2)

Linear Regression

Y’ = a + bX

Central Tendency

Population Mean
(Ungrouped data): μ=(∑x)/N

(Grouped Data): μ=(∑fx)/N

Sample Mean
(Ungrouped Data): ¯x = (∑x)/n

(Grouped Data): ¯x = (∑fx)/n

Median, Mode

Dispersion

1. Range
2. Variance: Population and sample
3. Standard Deviation: Population and Sample

Subdivisions

Inferential/Descriptive Stats

Basic Terms

Population (N), Sample (n)

Types of variables

Qualitative (Non-numeric),
Quantitative (numeric): Discrete or Continuous

Types of Organisation of Data

Contingency Table, Frequency Distribution