In hypotheses testing, what is the level of significance?
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A. B. C. D. E.B
All the above a correct descriptions of the level of significance.
In hypothesis testing, the level of significance, also known as the significance level or alpha (symbolized by the Greek letter "alpha"), is a predetermined threshold used to assess the strength of evidence against the null hypothesis. It is denoted by the Greek letter α.
The correct answer to the question is A. Symbolized by the Greek letter "alpha."
Now, let's delve into a detailed explanation of the significance level and its role in hypothesis testing:
Hypothesis testing is a statistical procedure used to make inferences or draw conclusions about a population based on a sample of data. It involves formulating a null hypothesis (H₀) and an alternative hypothesis (H₁), which represent conflicting statements about a population parameter (e.g., mean, proportion).
The null hypothesis (H₀) typically represents a statement of no effect or no difference, while the alternative hypothesis (H₁) suggests that there is a statistically significant effect or difference in the population.
To conduct a hypothesis test, we collect sample data and perform statistical calculations to determine the likelihood of obtaining the observed sample results if the null hypothesis were true. The level of significance comes into play when interpreting the results and making a decision about the null hypothesis.
The level of significance represents the maximum probability at which we are willing to reject the null hypothesis, assuming it is true. It is a predetermined value that helps us define the boundary for considering evidence against the null hypothesis.
Commonly used levels of significance include 0.05 (5%) and 0.01 (1%). These values are somewhat arbitrary but have become widely adopted in many fields of research.
When we set the level of significance at, for example, 0.05, it means we are willing to tolerate a 5% chance of making a Type I error. A Type I error occurs when we reject the null hypothesis when it is actually true. In other words, it represents the risk of falsely concluding that there is a significant effect or difference when there isn't one in the population.
To make a decision in hypothesis testing, we compare the p-value (probability value) calculated from the sample data with the level of significance. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value under the assumption that the null hypothesis is true.
If the p-value is less than or equal to the level of significance (e.g., p ≤ 0.05), we have sufficient evidence to reject the null hypothesis. We conclude that the observed results are unlikely to have occurred by chance alone, and we favor the alternative hypothesis.
On the other hand, if the p-value is greater than the level of significance (e.g., p > 0.05), we fail to reject the null hypothesis. We conclude that the observed results are reasonably likely to have occurred by chance, and we do not have enough evidence to support the alternative hypothesis.
In summary, the level of significance plays a crucial role in hypothesis testing by providing a threshold for accepting or rejecting the null hypothesis. It is symbolized by the Greek letter "alpha" (α) and represents the maximum probability of making a Type I error.