Question

A t-value of -5 is:

• A. Less important than a value of +5
• B. More important than a value of +5
• C. Equivalent to a value of +5
• D. Less significant than a value of +5

Hint:

For all symmetric statistical distributions (including the Z-distribution and t-distribution):
- The positive or negative sign indicates only the direction of the difference.
- The absolute value of the statistic determines the level of statistical significance.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In hypothesis testing, Student's t-distribution is a continuous probability distribution that is symmetric about a mean of zero.
The t-statistic measures how far a sample statistic deviates from the hypothesized null value in units of standard error.

Step 3: Detailed Explanation:
Let us analyze the statistical significance of positive and negative t-values:
- The t-distribution curve is bell-shaped and symmetric around its mean (\(\mu = 0\)).
- A positive t-value (such as \(+5\)) indicates that the sample mean is 5 standard errors above the hypothesized mean.
- A negative t-value (such as \(-5\)) indicates that the sample mean is 5 standard errors below the hypothesized mean.
- When performing a two-tailed hypothesis test, we evaluate the absolute value of the t-statistic:
\[ |t| = |-5| = |+5| = 5 \] - Because the distribution is symmetric, both \(t = -5\) and \(t = +5\) lie at the same distance from the center, corresponding to the exact same critical region and p-value.
- Therefore, they represent the same strength of evidence and are equivalent in statistical significance against the null hypothesis.
- The negative sign simply indicates the direction of the difference, not a lower level of significance or importance.
Thus, a t-value of \(-5\) is equivalent to a value of \(+5\).

Step 4: Final Answer:
In terms of statistical significance, a t-value of -5 is equivalent to a value of +5, matching Option (C).