Which of the following statements are TRUE with respect to the application of t-distribution for testing of Hypothesis?
A. It is a Non-parametric test B. It tests whether sample mean differs significantly from the population mean C. It tests the significance of an observed correlation coefficient D. It tests the significance of an observed covariation E. It tests the significance of an observed regression coefficient

Correct option is D

1. Statement A:
· Incorrect. The t-test is a parametric test, meaning it assumes specific properties about the population distribution, such as normality.
2. Statement B:
· Incorrect. Although a t-test can evaluate the sample mean against the population mean, the statement does not directly address the primary applications of the t-distribution in testing multiple hypothesis scenarios.
3. Statement C:
· Correct. The t-distribution is used to test the significance of an observed correlation coefficient, especially in cases of small sample sizes.
4. Statement D:
· Correct. Covariation refers to the joint variability of two variables, and the t-distribution can assess this through statistical testing.
5. Statement E:
· Correct. The t-distribution is used extensively in regression analysis to determine the significance of regression coefficients, ensuring that the predictor variables significantly influence the dependent variable.
Information Booster: 1. t-Distribution Characteristics:
· Used for small sample sizes (<30).
· Accounts for increased variability due to smaller sample sizes.
· Shape becomes closer to a normal distribution as sample size increases.
2. Applications:
· Hypothesis testing for means and regression coefficients.
· Confidence interval estimation for small samples.
· Testing the strength of correlations in small datasets.
3. Significance of Correlation:
· Uses t-distribution to determine whether an observed correlation is statistically significant and not due to random chance.
4. Testing Regression Coefficients:
· Individual coefficients in regression models are tested using a t-statistic to check their contribution to the model's predictive ability.
5. Covariation Testing:
· Statistical tests involving the relationship between two variables can use the t-distribution in some cases.