Hypothesis Testing

H. Kemal Ilter
2020

Concepts

1. The null hypothesis [math]H_0[/math] is a claim about the value of a population parameter. The alternate hypothesis [math]H_1[/math] is a claim opposite to [math]H_0[/math].
2. A test of hypothesis is a method for using sample data to decide whether to reject [math]H_0[/math]. [math]H_0[/math] will be assumed to be true until the sample evidence suggest otherwise.
3. A test statistic is a function of the sample data on which the decision is to be based.
4. A rejection region is the set of all values of a test statistic for which [math]H_0[/math] is rejected.
5. Type I error: you reject [math]H_0[/math] when [math]H_0[/math] is true. [math]P(\text{Type I error}) = P(\text{reject }H_0 \mid H_0\text{ true}) = \alpha[/math]. The resulting [math]\alpha[/math] is called the significance level of the test and the corresponding test is called a level [math]\alpha[/math] test. We will use test procedures that give [math]\alpha[/math] less than a specified level (0.05 or 0.01).

A Problem

I believe that dogs are as smart as people. Assume IQ of a dog follows [math]Xi \sim N(\mu,102)[/math]. IQ of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100, 60. We want to test if dogs are as smart as people by testing

H0 :μ=100vs. H1 :μ<100.

One reasonable thing one may try is to see how high the sample mean is.

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References