Match List I with List II: List I List II A. H0: μ = μ0 = 100 I. Alternative…
2022
Match List I with List II:
List I | List II |
|---|---|
A. H0: μ = μ0 = 100 | I. Alternative hypothesis: population mean is not equal to 100 |
B. Ha: μ ≠ μ0 | II. Alternative hypothesis: population mean is greater than 100 |
C. Ha: μ > μ0 | III. Null hypothesis: population mean equals hypothesised mean 100 |
D. Ha: μ < μ0 | IV. Alternative hypothesis: population mean is less than 100 |
Choose the correct answer from the options given below:
Answer: D. A-III, B-I, C-II, D-IV — ConceptIn hypothesis testing, the null hypothesis states equality with a hypothesised population value. A two-sided alternative uses “not equal to”, while…
- A.
A-II, B-IV, C-III, D-I
- B.
A-IV, B-III, C-I, D-II
- C.
A-I, B-III, C-IV, D-II
- D.
A-III, B-I, C-II, D-IV
Show answer & explanation
Correct answer: D
Concept
In hypothesis testing, the null hypothesis states equality with a hypothesised population value. A two-sided alternative uses “not equal to”, while right-tailed and left-tailed alternatives use “greater than” and “less than”, respectively.
Application
Statement | Meaning | Match |
|---|---|---|
H0: μ = 100 | The population mean equals the hypothesised value 100. | A–III |
Ha: μ ≠ 100 | The population mean is not equal to 100. | B–I |
Ha: μ > 100 | The population mean is greater than 100. | C–II |
Ha: μ < 100 | The population mean is less than 100. | D–IV |
Cross-check
The equality sign belongs to the null hypothesis, so A cannot represent an alternative hypothesis.
The symbol ≠ describes a two-sided alternative, so B pairs with I.
The symbols > and < define the right-tailed and left-tailed alternatives, so C pairs with II and D pairs with IV.
Result
Therefore, the matching is A–III, B–I, C–II, D–IV.