Hypothesis Tests – Poisson Distribution - Two tailed test
Hypothesis Tests – Poisson Distribution - Two tailed test
Understanding “Hypothesis Tests – Poisson Distribution - Two-tailed Test”
- A two-tailed test is a statistical test in which the rejection region is on both sides of the sampling distribution.
- Under the Poisson distribution, a two-tailed test would be used when the null hypothesis specifies a certain value, and the alternative hypothesis is that the actual value is not equal to the specified value.
Key Properties and Measures under a Poisson Distribution
- Sampling distribution: The Poisson distribution is characterised by its mean (λ), which is also the variance of the distribution.
- Poisson distribution notation: A random variable ‘X’ under a Poisson distribution would be written as X~Pois(λ).
- Probability mass function: The probability of an event occurring ‘x’ times under a Poisson distribution can be represented with the formula P(X=x) = [λ^x * e^(-λ)] / x!, where e is approximately equal to 2.71828.
Understanding the Two-tailed Hypothesis Test for Poisson Distribution
- The null hypothesis (H0) for a two-tailed test typically states that the mean λ is equal to a certain value (λ0). It can be written as H0: λ = λ0.
- The alternative hypothesis (H1) then posits that the mean λ is not equal to λ0. This can be written as H1: λ ≠ λ0.
- To reject the null hypothesis, the test statistic should fall in the critical region at either end of the distribution.
Applying the Two-tailed Hypothesis Test to Real-life Contexts
- Hypothesis tests, including the two-tailed Poisson test, can be used in diverse fields such as physics, engineering, and economics.
- For instance, an economist might use this test to determine whether the average number of sales in a company has changed after implementing a new marketing strategy.
Key Points to Remember
- It’s crucial to determine whether you’re executing a one-tailed (lower or upper) or two-tailed test when performing statistical hypothesis testing.
- Formulate your null and alternative hypotheses with care. Interchanging them could lead to the incorrect interpretation of results.
- Use the appropriate formula to calculate the test statistic, and compare it with the critical value.
- After obtaining the result, be sure to draw the correct conclusion based on whether your test statistic is in the critical region.
- Being familiar with hypothesis tests, specifically under Poisson distribution, can enhance your ability to make informed decisions supported by data.