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Poisson & Geometric Hypothesis Testing (Edexcel A-Level Further Mathematics): Quizzes

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Poisson Hypothesis Testing

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In a Poisson distribution $X \sim \text{Po}(\lambda)$ , what does $\lambda$ represent?

Mean and variance

What is the general form of the null hypothesis in Poisson hypothesis testing?

$H_0: \lambda = \lambda_0$

Which alternative hypothesis indicates a one-tailed test for a decrease in $\lambda$ ?

$H_1: \lambda < \lambda_0$

What alternative hypothesis is used for a two-tailed Poisson test?

$H_1: \lambda \neq \lambda_0$

What is the test statistic in Poisson hypothesis testing?

The observed value of $X$

What does the significance level $\alpha$ represent?

$P$ (reject $H_0$ | $H_0$ true)

In a two-tailed test with $\alpha = 0.10$ , how much is allocated to each tail?

0.05

If $P(X \leq 1) = 0.0404$ and $\alpha = 0.05$ , is $X \leq 1$ the critical region?

Yes

For $X \sim \text{Po}(8)$ in a two-tailed test at 10%, what is the critical region?

$X \leq 4$ or $X \geq 12$

If the test statistic is not in the critical region, what is the conclusion?

Insufficient evidence to reject $H_0$

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