A researcher wants to test whether a population mean is lower than a…
2024
A researcher wants to test whether a population mean is lower than a hypothesized value. Which test direction should be used?
Answer: B. Left-tailed test — Concept: In a one-sided hypothesis test, the direction of the alternative hypothesis determines the rejection tail. An alternative of the form μ < μ0 assigns…
- A.
Z-test
- B.
Left-tailed test
- C.
Right-tailed test
- D.
F-test
Show answer & explanation
Correct answer: B
Concept: In a one-sided hypothesis test, the direction of the alternative hypothesis determines the rejection tail. An alternative of the form μ < μ0 assigns sufficiently small test-statistic values to the rejection region, while μ > μ0 assigns sufficiently large values.
Application: Here the claim is μ < μ0. Therefore, observations far below the hypothesized mean produce test statistics in the lower, or left, tail of the sampling distribution.
Contrast:
A Z-test names a possible test statistic and reference distribution; its name alone does not specify the tail direction.
A right-tailed test represents an upper-direction alternative such as μ > μ0.
An F-test uses an F-ratio, commonly for variance comparisons or model tests; its name does not represent this lower-direction alternative.
Cross-check: As the sample mean moves increasingly below μ0, its standardized test statistic becomes more negative, placing the critical region on the left. Hence, the required direction is a left-tailed test.