Student's t-test is useful for which of the following purposes? A. Comparing…
2024
Student's t-test is useful for which of the following purposes?
A. Comparing the means of two groups to determine whether they differ significantly.
B. Comparing the means of more than two groups in one omnibus test to determine whether they differ significantly.
C. Testing the significance of a correlation coefficient.
D. Testing the significance of a regression coefficient.
Choose the most appropriate combination from the options below.
Answer: C. Only A, C and D — CONCEPTA t-test evaluates a standardized difference or coefficient relative to its standard error when the relevant population variance is estimated from…
- A.
Only A, B and C
- B.
Only B and D
- C.
Only A, C and D
- D.
Only A, B, C and D
Show answer & explanation
Correct answer: C
CONCEPT
A t-test evaluates a standardized difference or coefficient relative to its standard error when the relevant population variance is estimated from sample data.
It is suited to a two-mean comparison or to testing one model parameter. A simultaneous comparison of more than two means is ordinarily handled by an omnibus analysis of variance (ANOVA).
APPLICATION
Statement A: An independent-samples t-test can compare the means of two groups, subject to its assumptions.
Statement B: Comparing more than two group means with one overall test is an ANOVA problem; repeated pairwise t-tests inflate the family-wise Type I error rate.
Statement C: For a sample correlation r, a t statistic can test the null hypothesis that the population correlation is zero.
Statement D: A regression coefficient divided by its standard error gives a t statistic for testing whether that coefficient differs from a hypothesized value, commonly zero.
CROSS-CHECK
A, C and D each reduce to a two-mean or single-parameter t test. B alone asks for a joint comparison across more than two means, which calls for an omnibus F test in ANOVA.
Therefore, the applicable statements are A, C and D.