Statistics (Section E)

What is hypothesis testing?

The process of making inferences about population parameters based on sample statistics.

What does the null hypothesis (H₀) represent?

A statement that there is no effect, difference, or relationship; it represents the status quo.

What does the alternative hypothesis (H₁) suggest?

It contradicts the null hypothesis, suggesting there is an effect, difference, or relationship.

What does the significance level (α) indicate?

The probability of rejecting the null hypothesis when it is true (Type I error).

What are common significance level values?

0.05 (5%), 0.01 (1%), and 0.10 (10%).

What is a Z-test used for?

For normally distributed data with known population variance.

What is a T-test used for?

For normally distributed data with unknown population variance.

What is the critical region?

The set of values for the test statistic that leads to rejection of the null hypothesis.

What is the critical value?

The value that separates the critical region from the acceptance region.

What does a p-value represent?

The probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true.

What is the decision rule regarding the p-value and significance level?

If p-value < significance level, reject H₀.

What is a Type I Error?

Rejecting H₀ when it is true (false positive).

What is a Type II Error?

Not rejecting H₀ when it is false (false negative).

What formula is used for a One-Sample Z-Test?

z = (x̄ - μ) / (σ/√n).

When is the Two-Sample T-Test used?

To compare two population means when the population standard deviations are unknown.

What formula is used for the Chi-Squared Goodness-of-Fit Test?

χ² = Σ [(Observed - Expected)² / Expected].

What is the first step in the Hypothesis Testing Procedure?

State the hypotheses: Null hypothesis (H₀) and Alternative hypothesis (H₁).

What should you ensure about your data before conducting a hypothesis test?

That your data meets the assumptions of the test you're using.

What should be included in your conclusion after hypothesis testing?

State the conclusion in the context of the original problem.

How does sample size affect hypothesis testing results?

Larger samples give more reliable results.