Part 1. Basic Concepts of Statistics

Basic Concepts of Statistics
• Every four years, we suffer through an affliction, the presidential election. • Months before the election, public media will inform us that a poll conducted by the opinion research shows that a candidate gains support of more than 50 percent of voters.

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Basic Concepts of Statistics
• However, the high percent of support will be with a margin of error of plus or minus 3%. • What is meant by the term margin of error? • If you have an ambition to become president, you need to know something about statistics. • If you cannot perform statistics yourself, it would be better to hire a statistician right away.
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Testing Hypotheses: One-sample tests
• One-sample tests • Null hypothesis:
– Ho: μ ≧0

• Alternative hypothesis:
– Ha: μ ＜0

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What is a Hypothesis?
• A hypothesis is a claim (assumption) about a population parameter:
– population mean
Example: The mean monthly cell phone bill in this city is μ = $42

The Null Hypothesis, H0
• States the claim or assertion to be tested
Example: The average number of TV sets in U.S. Homes is equal to three (H0 : µ = 3 )

• Is always about a population parameter, not about a sample statistic
H0 : X = 3
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– population proportion
Example: The proportion of adults in this city with cell phones is π = 0.68
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H0 : µ = 3

The Null Hypothesis, H0
(continued)

The Alternative Hypothesis, H1
• Is the opposite of the null hypothesis
– e.g., The average number of TV sets in U.S. homes is not equal to 3 ( H1: μ ≠ 3 )

• Begin with the assumption that the null hypothesis is true – Similar to the notion of innocent until proven guilty • Refers to the status quo or historical value • Always contains “=” , “≤” or “≥” sign ≥ • May or may not be rejected
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• • • •

Challenges the status quo Never contains the “=” , “≤”