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Dr. Avishek Chakraborty

Visiting Assistant Professor Department of Statistics Texas A&M University

Using sample data to draw a conclusion about a population

• Statistical inference provides methods for drawing conclusions about a population from sample data. • Two key methods of statistical inference: o o

Confidence intervals

Hypothesis tests (a.k.a., tests of significance)

Hypothesis Testing: Evaluating the effectiveness of new machinery at the Bloggs Chemical Plant

• Before the installation of new machinery, long historical records revealed that the daily yield of fertilizer produced by the Bloggs Chemical Plant had a mean μ = 880 tons and a standard deviation σ = 21 tons. Some new machinery is being evaluated with the aim of increasing the daily mean yield without changing the population standard deviation σ.

Hypothesis Testing: Evaluating the effectiveness of new machinery at the Bloggs Chemical Plant

Null hypotheses

• The claim tested by a statistical test is called the null hypothesis. The test is designed to assess the strength of the evidence against the null hypothesis. Usually the null hypothesis is a statement of “no effect” or “no difference”, that is, a statement of the status quo.

Alternative hypotheses

• The claim about the population that we are trying to find evidence for is the alternative hypothesis. The alternative hypothesis is one-sided if it states that a parameter is larger than or that it is smaller than the null hypothesis value. It is two-sided if it states that the parameter is different from the null value (i.e., it could be either smaller or larger).

Null and alternative hypotheses

• The hypotheses should express the theories or suspicions we have before we see the data. It is cheating to first look at the data, and then frame hypotheses to fit what the data

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