Q: What is the difference between One-Tailed and Two-Tailed tests?

A two-tailed test checks for any difference (greater than or less than) from the null hypothesis, splitting your alpha level across both ends of the bell curve. A one-tailed (left or right) test strictly checks for a difference in only one specific direction, pushing the entire alpha probability into a single tail.

Q: What does 'Fail to Reject the Null Hypothesis' mean?

Statisticians do not say 'accept the null hypothesis' because you cannot definitively prove a negative. 'Failing to reject' simply means your current data experiment did not produce enough evidence to confidently declare a significant difference exists — it was likely random chance.

Question 1

What is a P-Value?

Accepted Answer

A P-value (probability value) is a number describing how likely it is that your data would have occurred by random chance, specifically assuming that the null hypothesis (H₀) is true. A small p-value indicates strong evidence against the null hypothesis, meaning the observed difference is statistically significant.

Question 2

What is the Significance Level (Alpha or α)?

Accepted Answer

Alpha (α) is your chosen threshold for statistical significance, most commonly set to 0.05. It represents a 5% risk of concluding that a difference exists when there is no actual difference (a False Positive or Type I error). If your calculated p-value is less than or equal to this alpha, you reject the null hypothesis.

Question 3

When should I use a Z-Score vs a T-Score?

Accepted Answer

You should use a Z-Score when your sample size is large (typically n > 30) AND the population standard deviation is known. You should use a T-Score (Student's t-test) when the sample size is small (n < 30) or the population standard deviation is unknown.

Question 4

What is the difference between One-Tailed and Two-Tailed tests?

Accepted Answer

A two-tailed test checks for any difference (greater than or less than) from the null hypothesis, splitting your alpha level across both ends of the bell curve. A one-tailed (left or right) test strictly checks for a difference in only one specific direction, pushing the entire alpha probability into a single tail.

Question 5

What does 'Fail to Reject the Null Hypothesis' mean?

Accepted Answer

Statisticians do not say 'accept the null hypothesis' because you cannot definitively prove a negative. 'Failing to reject' simply means your current data experiment did not produce enough evidence to confidently declare a significant difference exists — it was likely random chance.

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