Hypothesis Testing Fundamentals

Hypothesis Testing

Null and Alternative Hypotheses

• Null Hypothesis (H0): A statement of no effect or no difference.
  • Example: There is no significant difference in the average score of students who received additional tutoring and those who did not.
• Alternative Hypothesis (H1): A statement of an effect or difference.
  • Example: There is a significant difference in the average score of students who received additional tutoring and those who did not.
• Direction of the Alternative Hypothesis: One-tailed (directional) or two-tailed (non-directional)

Confidence Intervals

• Definition: A range of values within which the true population parameter is likely to lie.
• Interpretation: A (1 - α)100% confidence interval for a population parameter is an interval that has a (1 - α) probability of containing the true population parameter.
• Example: A 95% confidence interval for the population mean is (10, 15). This means that there is a 95% probability that the true population mean lies between 10 and 15.

T-tests

• Independent Samples T-test: Compares the means of two independent groups.
• Paired Samples T-test: Compares the means of two related groups (e.g., before and after treatment).
• One Sample T-test: Compares the mean of one group to a known population mean.

P-values

• Definition: The probability of obtaining a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true.
• Interpretation:
  • If p-value ≤ α (significance level), reject the null hypothesis.
  • If p-value > α, fail to reject the null hypothesis.
• Example: If the p-value is 0.01 and α = 0.05, reject the null hypothesis because 0.01 ≤ 0.05.

Normal Distribution

• Definition: A continuous probability distribution with a symmetrical bell-shaped curve.
• Properties:
  • Mean (μ) = Median = Mode
  • Symmetrical around the mean
  • Bell-shaped curve
• Importance in Hypothesis Testing: Many statistical tests assume normality of the data or the sampling distribution of the test statistic.

Understand the basics of hypothesis testing, including null and alternative hypotheses, confidence intervals, t-tests, p-values, and the importance of normal distribution in statistical testing.