Small Samples Test of significance is based on

The correct answer is - All of the above

Key Points

• Small Samples Test of significance
  • Involves statistical methods used to determine if there is a significant difference between sample means or proportions.
  • Is typically employed when the sample size is small (n < 30).
• Student's t-Distribution
  • Used for hypothesis testing when the sample size is small and the population standard deviation is unknown.
  • Commonly applied in t-tests for comparing the means of two groups.
• F-distribution
  • Used in analysis of variance (ANOVA) tests, which assess the differences between group variances.
  • Helps in comparing two variances to understand if they are significantly different.
• Fisher's Z-Distribution
  • Used in the context of correlation coefficients.
  • Helps in testing the significance of the difference between two correlation coefficients.

Additional Information

• Assumptions for Small Samples Test of significance
  • Data should be approximately normally distributed.
  • Sample should be randomly selected and representative of the population.
• t-Distribution Characteristics
  • Symmetrical and bell-shaped, similar to the normal distribution but with thicker tails.
  • As the sample size increases, the t-distribution approaches the normal distribution.
• ANOVA and F-distribution
  • ANOVA tests are useful for comparing three or more groups.
  • The F-distribution is right-skewed and used to derive critical values for the F-test.
• Fisher's Z-Transformation
  • Converts the sampling distribution of the correlation coefficient to a normal distribution.
  • Facilitates hypothesis testing and construction of confidence intervals for correlation coefficients.