Suppose H0 = null hypothesis, Ha = alternative hypothesis, μ = population…
2024
Suppose H0 = null hypothesis, Ha = alternative hypothesis, μ = population mean, and μ0 = hypothesized mean. A researcher sets up H0: μ = μ0 and Ha: μ < μ0. In this situation, which test would the researcher apply?
Answer: B. left-tailed test — ConceptIn a one-sample hypothesis test, the alternative hypothesis determines the direction of the rejection region. An alternative of the form μ < μ0 uses…
- A.
right-tailed test
- B.
left-tailed test
- C.
two-tailed test
- D.
half-tailed test
Show answer & explanation
Correct answer: B
Concept
In a one-sample hypothesis test, the alternative hypothesis determines the direction of the rejection region.
An alternative of the form μ < μ0 uses the lower tail; μ > μ0 uses the upper tail, and μ ≠ μ0 uses both tails.
Application
Read the alternative hypothesis: Ha: μ < μ0.
The less-than sign directs the rejection region toward values below μ0, which is the lower or left tail of the sampling distribution.
Therefore, the appropriate procedure is a left-tailed test.
Contrast
A right-tailed test corresponds to Ha: μ > μ0.
A two-tailed test corresponds to Ha: μ ≠ μ0.
Half-tailed test is not a standard hypothesis-testing classification.
Cross-check
Values substantially smaller than μ0 provide evidence for Ha, so only the left end of the distribution is the relevant rejection region. Hence, the result is left-tailed test.