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 :
Both Statement I and Statement II are false.
Let's examine the given statements about Type I and Type II errors in hypothesis testing. These types of errors are important concepts in statistics, particularly in the context of hypothesis testing.
- Statement I: "If we accept a hypothesis when it should be rejected, we say type I error has been made."
In hypothesis testing, a Type I error occurs when the null hypothesis is rejected when it is actually true. This is also known as a "false positive." Therefore, Statement I incorrectly describes a Type I error. This statement is false. - Statement II: "If we reject a hypothesis when it should be accepted, we say type II error has been made."
A Type II error occurs when we fail to reject the null hypothesis when it is actually false, meaning we accept the null hypothesis incorrectly when the alternative hypothesis is true. So, the error described in Statement II is when we accept the null hypothesis incorrectly, not reject it. Hence, Statement II is also false.
Based on the above analysis, both statements I and II are false. Therefore, the correct answer is: "Both Statement I and Statement II are false."
Similar Questions
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:
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.
