8 - Introduction to Hypothesis Testing Flashcards
(10 cards)
What is hypothesis testing?
Hypothesis testing is a statistical method used to make an educated guess about an assumption regarding a population based on the analysis of sample data. It helps determine the reliability of a study and test predictions derived from theories.
What are the two types of hypotheses in hypothesis testing?
The Null Hypothesis (H0) claims that there is no change or effect in the population parameter, while the Alternative Hypothesis (H1) asserts that there has been a change (increase, decrease, or difference).
Define ‘Statistic’ and ‘Parameter’.
A Statistic is a value calculated from sample data, used to estimate a population parameter. A Parameter is a measurable characteristic of a whole population, often unknown and estimated through sample statistics.
What steps are involved in preparing a hypothesis test?
The preparation involves defining the hypotheses, identifying the distribution (such as Binomial or Normal), and establishing the significance level.
How do you determine critical regions in hypothesis testing?
The critical region is defined based on the significance level (usually denoted as alpha, such as 0.05), and it indicates where the null hypothesis (H0) will be rejected if the test statistic falls within this region.
(All critical regions can be found in the formula booklet)
What is the significance of the significance level in hypothesis testing?
The significance level defines the probability of rejecting the null hypothesis when it is true (Type I error), helping to control the likelihood of false conclusions.
Q: How is the standard error calculated in relation to the sample mean
The Standard Error (SE) measures how far the sample mean (X̅) is likely to be from the population mean (μ). It is calculated as SE = σ/√n, where σ is the population standard deviation and n is the sample size
What constitutes a Type I error and a Type II error?
A Type I error occurs when the null hypothesis is rejected when it is true; conversely, a Type II error happens when the null hypothesis is not rejected when it is false.
In hypothesis testing, what is the role of the critical value?
The critical value is the threshold that defines the edges of the critical region; if the computed test statistic exceeds this value, the null hypothesis will be rejected.
Describe the steps for performing a hypothesis test.
The steps generally include: 1) Formulating the hypotheses, 2) Stating the assumed distribution, 3) Sketching the distribution, 4) Conducting calculations, 5) Comparing the results to the critical region or significance level, and 6) Drawing a conclusion based on the comparison.
