Business Statistics

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Business Statistics

Topic 1: Introduction

Types of Organisation of Data

Contingency Table, Frequency Distribution

Types of variables

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

Basic Terms

Population (N), Sample (n)

Subdivisions

Inferential/Descriptive Stats

Topic 2: Statistical Measures

Dispersion

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

Central Tendency

Median, Mode

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

(Grouped Data): ¯x = (∑fx)/n

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

(Grouped Data): μ=(∑fx)/N

Topic 3: Regression & Correlation Analysis

Linear Regression

Y’ = a + bX

Correlation Analysis

Coefficient of Determination (r2)

Coefficient of Correlation (r)

Negative, Positive, or No correlation

Topic 4: Probability Concepts

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

Terms: Experiment, Outcome, Sample Space, Event

Topic 5: Continuous Probability Concepts

Finding z-value z=(x-µ)/σ

Finding z-v

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

Normal Distribution: Mean = Median = Mode

Topic 9: Chi-Square Distribution

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

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

Types of Testing 1. Goodness-of-Fit Test

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

Topic 8: Hypothesis Testing

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

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: statement or assumption

Topic 7: Confidence Interval

Conditions

Population Normal?

Yes

Is σ known?

Yes, use z-distribution

No, Is n≥30?

Yes (CLT), Use z-distribution

No, Use t-distribution

No

Is n≥30?

Yes(CLT)

Use z-distribution

Interval Estimate: Uses intervals for estimation

Point Estimate (PE): Uses one value for estimation

's' is the PE of population standard deviation

sample mean is the PE of population mean

Topic 6: Sample Probabilities

Conditions of sample mean to be normal

Normal distribution (regardless of sample size)

Distribution unknown, n≥30

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.