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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
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– H0: μ = 50, H1: μ ≠ 50

The Hypothesis Testing Process
(continued)

• Sample the population and find sample mean. Population

• Suppose the sample mean age was X = 20. • This is significantly lower than the claimed mean population age of 50. • If the null hypothesis were true, the probability of getting such a different sample mean would be very small, so you reject the null hypothesis . • In other words, getting a sample mean of 20 is so unlikely if the population mean was 50, you conclude that the population mean must not be 50.
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Sample

The Hypothesis Testing Process (continued)
Sampling Distribution of X

The Test Statistic and Critical Values
• If the sample mean is close to the assumed population mean, the null hypothesis is not rejected. • If the sample mean is far from the assumed population mean, the null hypothesis is rejected.

20 If it is unlikely that you would get a sample mean of this value ...

X µ = 50 If H0 is true ... When in fact this were the population mean… ... then you reject the null hypothesis that µ = 50.

• How far is “far enough” to reject H0? • The critical value of a test statistic creates a “line in the sand” for decision making -- it answers the question of how far is far enough.
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The Test Statistic and Critical Values
Sampling Distribution of the test statistic

Level of Significance and the Rejection Region
H0:

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