Test

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PAS

Cegep/2

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199 words

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2 minutes

Experiment to prove a hypothesis

[!abstract] Rejection region
Set of possible values of the test statistic for which $H_0$ is rejected in favour of $H_1$

Tails

One-tailed test: test whose alternative hypothesis specifies the direction ($<$ or $>$)

$$\begin{array}{rl}P(T_{n-1}>t_{n-1,\alpha })& =1-\alpha \\ P(T_{n-1}<-t_{n-1,\alpha })& =1-\alpha \end{array}$$

Two-tailed test: test whose alternative hypothesis doesn't specify the direction ($\ne$)

$$\begin{array}{rl}P(-t_{n-1,\frac{\alpha }{2}}<T_{n-1}<t_{n-1,\frac{\alpha }{2}})& =1-\alpha \\ P(T_{n-1}<-t_{n-1,\frac{\alpha }{2}}\cup T_{n-1}>t_{n-1,\frac{\alpha }{2}})& =\alpha \end{array}$$

Examples

A random sample of 15 sections of sewer pipe are tested for strength. You choose α = 0.05. Suppose the mean is found to be 2500 pounds per linear foot and the standard deviation is 200 pounds per linear foot. What would your test that strength is above 2400 conclude?

$$\begin{array}{rl}{T}_{14}& =\frac{\bar{x}-\mu }{\frac{s}{\sqrt{n}}}\\ & =\frac{2500-2400}{\frac{200}{\sqrt{15}}}\\ & =1.93\end{array}$$

Therefore, there is sufficient evidence to reject $H_0$ at $\alpha =0.05$.

Contributors

Ajitani Hifumi

Changelog

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