Which of the following statements is true in the context of the testing of a hypothesis?
It is only the null hypothesis, that can be tested.
The question turns on a point that is easy to state loosely but precise in statistical procedure: which hypothesis the test is actually applied to.
It is only the null hypothesis that is directly tested. The reason is practical. A null hypothesis states a definite position - that there is no difference, or no relationship, or that a parameter equals a stated value - and this exactness makes it possible to work out the sampling distribution and to compute how likely the observed data would be if the hypothesis were true. The alternative hypothesis, by contrast, is usually indefinite: saying that a difference exists does not say how large it is, so no single sampling distribution follows from it and no probability can be computed against it.
The procedure therefore runs in a particular direction. The researcher sets up the null hypothesis, assumes it true, and asks how probable the observed result would be under that assumption. If that probability falls below the chosen level of significance, the null is rejected and the alternative is accepted by implication. The alternative is never itself put to the test; it is supported indirectly by the rejection of the null.
This also explains why a test never proves the null hypothesis. Failure to reject means only that the evidence was insufficient to overturn it.
Hence it is only the null hypothesis that can be tested.
Similar Questions
Given below are two statements :
Statement I : If we accept a hypothesis when it should be rejected, we say type I error has been made.
Statement II : If we reject a hypothesis when it should be accepted, we say type II error has been made.
In the light of the above statements, choose the most appropriate answer from the options given below :
Given below are two statements:
Statement-I The null hypothesis for testing of difference between means is generally stated as Ho: μ₁ ≠ μ₂, where (μ₁) and (μ₂) are the population means of the two populations, respectively.
Statement II: When samples happen to be small samples and population variances are not known but assumed to be equal, Z-test is employed for testing the null hypothesis.
In the light of the above statements, choose the most appropriate answer from the options given below:
At the stage of data analysis, in which quantitative techniques have been used by a researcher, the evidence warrants the rejection of Null Hypothesis (H₀). Which of the following decisions of the researcher will be deemed appropriate?
A researcher fails to reject the null hypothesis (Ho) in his/her research. What implications will it carry for his/her principal research hypothesis?
A hypothesis is:
After identifying the different variables and establishing the logical reasoning in theoretical framework, the next step in the research process is to
Male and female students perform equally well in a numerical aptitude test. This statement indicates a:
Important Questions from Hypothesis
Which one of the following is NOT a type of hypothesis?
Which one of the following possibilities leads to Type I error in hypothesis testing?
Population variance differ from sample variance in which of the following manner:
A. μ ± 3σ is replaced by x̅ + 9σ2
B. μ is replaced by x̅
C. μ2 is replaced by \(\rm \frac{\mu^2}{(n-1) α}\)
D. N is replaced by n - 1
E. N is replaced by n - 1 - α
Choose the correct answer from the options given below:
Which of the following hypotheses was propounded by Harry Hammond Hess in 1962?
- Which of the following statement is not the characteristics of hypothesis ?
(i) Hypothesis should be capable of testing
(ii) Hypothesis should be consistent with most known facts
(iii) Hypothesis should be unlimited in scope
(iv) Hypothesis should be amenable to testing beyond a reasonable time.
