Statistical Test Calculator

Test Types

• One-Sample t-Test: Compare sample mean to known population mean
• Two-Sample t-Test: Compare means of two independent samples
• Chi-Square Test: Test for association or goodness of fit
• z-Test: Like t-test but when population standard deviation is known

Key Concepts

• Null Hypothesis (H₀): Statement of no effect or difference
• Alternative Hypothesis (H₁): Statement of an effect or difference
• p-value: Probability of observing results if H₀ is true
• α (Alpha): Significance level, typically 0.05
• Critical Value: Threshold for rejecting H₀

Decision Rules

• If p-value ≤ α: Reject H₀ (statistically significant)
• If p-value > α: Fail to reject H₀ (not significant)
• If |test statistic| > critical value: Reject H₀
• Confidence Interval: Range of plausible values for parameter

Applications

• Quality Control: Testing if process meets specifications
• Medical Research: Comparing treatment effectiveness
• Market Research: Analyzing customer preferences
• Education: Comparing teaching methods