Probability and Statistics Multiple Choice Questions & Answers (MCQs) on “Testing of Hypothesis”.
1. A statement made about a population for testing purpose is called?
a) Statistic
b) Hypothesis
c) Level of Significance
d) Test-Statistic
Answer: b
Clarification: Hypothesis is a statement made about a population in general. It is then tested and correspondingly accepted if True and rejected if False.
2. If the assumed hypothesis is tested for rejection considering it to be true is called?
a) Null Hypothesis
b) Statistical Hypothesis
c) Simple Hypothesis
d) Composite Hypothesis
Answer: a
Clarification: If the assumed hypothesis is tested for rejection considering it to be true is called Null Hypothesis. It gives the value of population parameter.
3. A statement whose validity is tested on the basis of a sample is called?
a) Null Hypothesis
b) Statistical Hypothesis
c) Simple Hypothesis
d) Composite Hypothesis
Answer: b
Clarification: In testing of Hypothesis a statement whose validity is tested on the basis of a sample is called as Statistical Hypothesis. Its validity is tested with respect to a sample.
4. A hypothesis which defines the population distribution is called?
a) Null Hypothesis
b) Statistical Hypothesis
c) Simple Hypothesis
d) Composite Hypothesis
Answer: c
Clarification: A hypothesis which defines the population distribution is called as Simple hypothesis. It specifies all parameter values.
5. If the null hypothesis is false then which of the following is accepted?
a) Null Hypothesis
b) Positive Hypothesis
c) Negative Hypothesis
d) Alternative Hypothesis.
Answer: d
Clarification: If the null hypothesis is false then Alternative Hypothesis is accepted. It is also called as Research Hypothesis.
6. The rejection probability of Null Hypothesis when it is true is called as?
a) Level of Confidence
b) Level of Significance
c) Level of Margin
d) Level of Rejection
Answer: b
Clarification: Level of Significance is defined as the probability of rejection of a True Null Hypothesis. Below this probability a Null Hypothesis is rejected.
7. The point where the Null Hypothesis gets rejected is called as?
a) Significant Value
b) Rejection Value
c) Acceptance Value
d) Critical Value
Answer: d
Clarification: The point where the Null Hypothesis gets rejected is called as Critical Value. It is also called as dividing point for separation of the regions where hypothesis is accepted and rejected.
8. If the Critical region is evenly distributed then the test is referred as?
a) Two tailed
b) One tailed
c) Three tailed
d) Zero tailed
Answer: a
Clarification: In two tailed test the Critical region is evenly distributed. One region contains the area where Null Hypothesis is accepted and another contains the area where it is rejected.
9. The type of test is defined by which of the following?
a) Null Hypothesis
b) Simple Hypothesis
c) Alternative Hypothesis
d) Composite Hypothesis
Answer: c
Clarification: Alternative Hypothesis defines whether the test is one tailed or two tailed. It is also called as Research Hypothesis.
10. Which of the following is defined as the rule or formula to test a Null Hypothesis?
a) Test statistic
b) Population statistic
c) Variance statistic
d) Null statistic
Answer: a
Clarification: Test statistic provides a basis for testing a Null Hypothesis. A test statistic is a random variable that is calculated from sample data and used in a hypothesis test.
11. Consider a hypothesis H0 where ϕ0 = 5 against H1 where ϕ1 > 5. The test is?
a) Right tailed
b) Left tailed
c) Center tailed
d) Cross tailed
Answer: a
Clarification: In the given example since H1 lies to the right of the Ho that is the Null Hypothesis the test is referred as a Right tailed test.
12. Consider a hypothesis where H0 where ϕ0 = 23 against H1 where ϕ1 < 23. The test is?
a) Right tailed
b) Left tailed
c) Center tailed
d) Cross tailed
Answer: b
Clarification: In the Normal Distribution curve of both the hypothesis the H1 hypothesis lies to the left of the Null hypothesis hence the test is a Left tailed.
13. Type 1 error occurs when?
a) We reject H0 if it is True
b) We reject H0 if it is False
c) We accept H0 if it is True
d) We accept H0 if it is False
Answer: a
Clarification: In Testing of Hypothesis Type 1 error occurs when we reject H0 if it is True. On the contrary a Type 2 error occurs when we accept H0 if it is False.
14. The probability of Type 1 error is referred as?
a) 1-α
b) β
c) α
d) 1-β
Answer: c
Clarification: In Testing of Hypothesis Type 1 error occurs when we reject H0 if it is True. The probability of H0 is α then the error probability will be 1- α.
15. Alternative Hypothesis is also called as?
a) Composite hypothesis
b) Research Hypothesis
c) Simple Hypothesis
d) Null Hypothesis
Answer: b
Clarification: Alternative Hypothesis is also called as Research Hypothesis. If the Null Hypothesis is false then Alternative Hypothesis is accepted.