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:
Both Statement I and Statement II are false.
Let's analyze each statement:
- Statement I: The statement claims that the null hypothesis for testing the difference between means is generally stated as \( H_0: \mu_1 \neq \mu_2 \), where \( \mu_1 \) and \( \mu_2 \) are the population means of two populations.
- The standard null hypothesis for testing the difference between means is usually stated as \( H_0: \mu_1 = \mu_2 \), indicating no difference between the two population means. Thus, Statement I is false.
- Statement II: It states that when the samples are small and population variances are not known but assumed to be equal, a Z-test is employed for testing the null hypothesis.
- In fact, when dealing with small sample sizes and unknown population variances that are assumed to be equal, a t-test (specifically, a two-sample t-test) is more appropriate, not a Z-test. Hence, Statement II is also false.
Conclusion: Both Statement I and Statement II are false. Therefore, the correct answer is the option: Both Statement I and Statement II are false.
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 :
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:
Which of the following statements is true in the context of the testing of a hypothesis?
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.
