Final answer:
The null hypothesis represents the position of no difference, against which the alternative hypothesis is tested. P-values are used to decide whether to reject the null hypothesis. The width of a confidence interval is inversely related to the confidence level.
Step-by-step explanation:
In the context of hypothesis testing, the null hypothesis (H₀) represents a position of no effect or no difference, and it is what we initially assume to be true. The alternative hypothesis (H₁) represents the outcome that the research is aiming to support, indicating that there is an effect or a difference.
For example, if a study is to determine if the true proportion of people in a town suffering from a certain disease is lower than the national average, H₀ would state that the proportion in the town is equal to or greater than the national average, while H₁ would state that the proportion in the town is lower than the national average.
When you perform a hypothesis test, if the p-value is lower than the chosen significance level (alpha), then you would reject the null hypothesis. This decision suggests that there is enough evidence to support the alternative hypothesis.
The confidence interval provides a range within which we can be confident that the true parameter lies, with a specified level of confidence, such as 95% or 99%. As the confidence level decreases, the confidence interval becomes narrower, indicating less uncertainty but also less confidence in the estimate.