Testing of Hypothesis MCQ Quiz - Objective Question with Answer for Testing of Hypothesis - Download Free PDF

The correct answer is - Option 4

Key Points

• (A) A good hypothesis is based on sound reasoning that is consistent with theory or previous research.
  • This emphasizes the importance of forming hypotheses that are grounded in established knowledge and logical reasoning.
  • Ensures the hypothesis is credible and testable within the framework of existing theory.
• (D) Qualitative researchers may develop guiding hypothesis for the proposed research.
  • In qualitative research, hypotheses often guide the study and provide direction, though they may be more flexible and evolving compared to quantitative research.
  • Helps in setting a preliminary focus while allowing for exploration and discovery during the research process.

Additional Information

• (B) A deductive hypothesis is a generalization based on specific observations.
  • This statement is incorrect. A deductive hypothesis works the other way around: it starts with a general theory and tests hypotheses derived from it.
• (C) Tenth grade biology students who are instructed using interactive multimedia achieve at higher level than those who receive regular instruction only is an example of non-directional hypothesis.
  • This statement is incorrect. This is an example of a directional hypothesis because it predicts a specific outcome (higher achievement with interactive multimedia).

The correct answer is 'Rejecting the null hypothesis when it is true'

Key Points

• Type I Error:
  • A Type I error, also known as a false positive, occurs when the null hypothesis is true, but it is incorrectly rejected. In other words, it indicates that an effect or relationship exists when it actually does not.
  • This type of error can lead to incorrect conclusions and actions based on the belief that a particular effect or difference exists when it does not.
  • Type I error is denoted by the Greek letter alpha (α), which represents the significance level of the test. Common alpha levels are 0.05, 0.01, and 0.10.

Additional Information

• Failing to reject the null hypothesis, when the alternative hypothesis is true:
  • This describes a Type II error, also known as a false negative. In this case, the null hypothesis is not rejected even though the alternative hypothesis is true.
  • Type II error is denoted by the Greek letter beta (β), and it represents the probability of failing to detect an effect or difference when one actually exists.
• It depends on data analysis:
  • While data analysis can influence the likelihood of making Type I or Type II errors, the definition of Type I error specifically pertains to rejecting the null hypothesis when it is true.
  • The accuracy of data analysis can affect the results, but it does not change the fundamental definition of Type I error.
• Both (1) and (2) above:
  • This option is incorrect because it combines the definitions of both Type I and Type II errors, which are distinct and separate concepts in statistical hypothesis testing.
  • Type I error is specifically about rejecting a true null hypothesis, while Type II error is about failing to reject a false null hypothesis.

The correct answer is 'Accept a false null hypothesis'

Key Points

• Type-II error in statistical inference:
  • A Type-II error occurs when we fail to reject a false null hypothesis, essentially 'accepting' it. This means that there is an effect or difference, but the test fails to detect it.
  • This type of error is also known as a false negative, meaning we conclude there is no effect when there actually is one.
  • The probability of committing a Type-II error is denoted by beta (β), and it is inversely related to the power of the test (1 - β).

Additional Information

• Other options explained:
  • Accept a true null hypothesis: This means correctly identifying that there is no effect or difference when there truly is none. This is not an error.
  • Reject a true null hypothesis: This is a Type-I error, also known as a false positive, where we incorrectly conclude there is an effect when there is none.
  • Reject a false null hypothesis: This is the correct decision, indicating that we have correctly identified an effect or difference when one exists. This is not an error.

The correct answer is B, C, and D only.

Key Points

• Hypothesis:
  • A hypothesis is a tentative statement or prediction that can be tested by scientific research.
  • It is an essential component of the scientific method, allowing researchers to make predictions that can be tested through experiments and observations.
• Correct Statements:
  • Snow (1973) described six levels of theory, with the first level being hypothesis formation (B):
    • This statement is true as Snow's theory includes hypothesis formation as the initial level of scientific inquiry.
  • For the hypothesis to be testable, the variables must be operationally defined (C):
    • Operational definitions specify the exact procedures used to measure or manipulate variables, making it possible to test the hypothesis.
  • The most common use of hypothesis is to test whether an existing theory can be used to solve a problem (D):
    • Hypotheses often derive from existing theories and are used to test the validity and applicability of these theories in specific situations.

Additional Information

• Incorrect Statements:
  • The minor premise of the older deductive method was gradually replaced by hypothesis (A):
    • This statement is incorrect because the minor premise in deductive reasoning is not necessarily replaced by a hypothesis. Deductive reasoning and hypothesis formation are different aspects of scientific methodology.
  • The hypothesis focuses the investigation on indefinite targets (E):
    • This statement is incorrect because a hypothesis actually aims to focus the investigation on specific, testable predictions, not indefinite targets.

The correct answer is a - 1,2, b - 3,4, c - 5.

Key Points The correct sequence is:

• Non-sampling errors- Law of statistical regularity and the law of inertia of large numbers.
• Sampling techniques- Quota sampling and response errors.
• Theoretical basis of sampling- Nonresponse errors.

Important Points Non-sampling errors: This refers to all sorts of errors that are not related to any sampling techniques or the sample collected. This kind of error occurs due to data collection which causes data to differ in terms of values.

Law of statistical regularity: This law states that if a large number of samples is selected from a larger group of people then, those samples will represent the characteristics of a larger group of people.

Law of inertia of large numbers: This law states that the larger sample of people represents more accurate results. Larger samples are more stable and consistent.

Quota sampling: It is a non-probabilistic sampling where there is a non-random selection of a proportionate number of units based on a certain quota.

Response errors: These kinds of errors are based on the responses collected during research. This might occur due to different factors like interview questions or the questionnaire.

Nonresponse error: It refers to not getting accurate results after surveying the whole population. The researcher then uses bias while taking the survey.

Hence, the correct answer is a - 1,2, b - 3,4, c - 5.

Hypothesis testing

It uses sample data to make inferences about the population.

It gives tremendous benefits by working on random samples, as it is practically impossible to measure the entire population.

Hypothesis testing is a procedure that assesses two mutually exclusive theories about the properties of a population.

 For a Hypothesis testing, the two hypotheses are as follows:

1. Null Hypothesis

2. Alternative hypothesis

There are two errors defined, both are for null hypothesis condition

1. Type I error

2. Type II error

Hence from the above table, we can see, the Type II error accepts the null hypothesis when the test fails and thus it should be rejected.

Errors In Hypothesis Testing

Type-I error corresponds to rejecting H₀ (Null hypothesis) when H₀ is actually true, and a Type-II error corresponds to accepting H₀ (Null hypothesis)when H₀ is false. Hence four possibilities may arise.

1. The null hypothesis is true but the test rejects it (Type-I error).
2. The null hypothesis is false but the test accepts it (Type-II error).
3. The null hypothesis is true and the test accepts it (correct decision).
4. The null hypothesis is false and test rejects it (correct decision)

1) Type-I Error:

• In a hypothesis test, a Type-I error occurs when the null hypothesis is rejected when it is in fact true. That is, H₀ is wrongly rejected. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug. That is, there is no difference between the two drugs on average.
• A Type-I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them. A Type-I error is often considered to be more serious, and therefore more important to avoid than a Type-II error.
• The exact probability of a Type-I error is generally unknown. If we do not reject the null hypothesis, it may still be false (a Type-I error) as the sample may not be big enough to identify the falseness of the null hypothesis (especially if the truth is very close to the hypothesis).

Important Points

2) Type-II Error

• In a hypothesis test, a Type-II error occurs when the null hypothesis, H₀, is not rejected when it is in fact false.
• For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug; that is Ho: there is no difference between the two drugs on average.
• A Type-II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different effects.
• A Type-II error is frequently due to sample sizes being too small.
• The probability of a Type-II error is symbolized by â and written: P (Type-II error) = â (but is generally unknown).
• A Type-II error can also be referred to as an error of the second kind.

​Hence, An investigator commits type II error when he/she accepts a null hypothesis when it is false.

t-test : t- test is a statistical term which is used to define the significant difference between two groups, the differences are measured in terms of means of the groups.

Significant difference: Significant differences in statistics means measurable differences.

Hypothesis testing

• It uses sample data to make inferences about the population.
• It gives tremendous benefits by working on random samples, as it is practically impossible to measure the entire population.
• Hypothesis testing is a procedure that assesses two mutually exclusive theories about the properties of a population.
• For Hypothesis testing, the two hypotheses are as follows:
  • Null Hypothesis
  • Alternative hypothesis
• In null hypothesis significance testing, the p-value is the probability that an observed difference could have occurred just by random chance when it is assumed that the null hypothesis is correct.

Important Points

• The significance level for a given hypothesis test is a value for which a P-value less than or equal to is considered statistically significant. E.g. p-values are 0.1, 0.05 and 0.01.
• If its given t-value to be significant at 0.1 means chances are 1 out of 100 that the difference between means has occurred due to sampling errors.
• From abo ve explanation, Chances are 5 out of 100 that the difference between means has occurred due to sampling errors.

Hence, A researcher used t-test to compare two means based on independent samples and found the t-value to be significant at 0.05 level. This means that Chances are 5 out of 100 that the difference between means has occurred due to sampling errors.

Ans: Option 1

Additional Information:

Two samples are independent if the samples from one population is not related or cannot be paired with sample from another group. Independent samples are randomly selected.

• Errors in hypothesis testing: There are two errors defined, both are for null hypothesis condition

1. Type-I error corresponds to rejecting H₀ (Null hypothesis) when H0 is actually true, and a 
2. Type -II error corresponds to accepting H0 (Null hypothesis)when H0 is false. Hence four possibilities may arise:

• The null hypothesis is true but the test rejects it (Type-I error).
• The null hypothesis is false but the test accepts it (Type-II error).
• The null hypothesis is true and the test accepts it (correct decision).
• The null hypothesis is false and the test rejects it (correct decision)

​

t-test : t- test is a statistical term which is used to define the significant difference between two groups, the differences are measured in terms of means of the groups.

Hypothesis testing

• It uses sample data to make inferences about the population.
• It gives tremendous benefits by working on random samples, as it is practically impossible to measure the entire population.
• Hypothesis testing is a procedure that assesses two mutually exclusive theories about the properties of a population.
•  For Hypothesis testing, the two hypotheses are as follows:

1. Null Hypothesis
2. Alternative hypothesis

• There are two errors defined, both are for null hypothesis condition

• Type-I error corresponds to rejecting H0 (Null hypothesis) when H0 is actually true, and a Type-II error corresponds to accepting H0 (Null hypothesis)when H0 is false. Hence four possibilities may arise:

  • The null hypothesis is true but the test rejects it (Type-I error).
  • The null hypothesis is false but the test accepts it (Type-II error).
  • The null hypothesis is true and the test accepts it (correct decision).
  • The null hypothesis is false and test rejects it (correct decision)

Significant difference: Significant differences in statistics means measurable differences.

Given: 

Error Type: Type I error

Experiment done: 20 times

Significant difference: 19 times

To find: Probability of type I error

Terms:

Formula: Probability = No of favourable outcome/Total no of outcome

Calculation:

Probability= No of favourable outcome/Total no of outcome

Since we want to find the probability of type I error, we will calculate the total number of cases (= 20) and  number of cases in favour of type I error or which not significant (20-19=1)

Probability= No of favourable outcome(in favour of type I error) /Total no of outcome (cases) 

                 = 1/20

                 = 0.05

Hence, The probability of committing a type I error was 0.05

The correct answer is Accepting an incorrect hypothesis.

Key Points

•  Type II error is accepting an incorrect hypothesis.
• In statistics, a type II error is the error of failing to reject a false null hypothesis. This means that the researcher concludes that there is no difference between the groups being studied, when in reality there is a difference.
• Type II errors are often called false negatives. They can occur when the sample size is too small, the power of the test is too low, or when the effect size is small.

Additional Information Here is an example of a type II error:

A researcher is testing a new drug to see if it is effective in reducing blood pressure. The researcher conducts a study and finds that there is no statistically significant difference between the blood pressure of the group that took the drug and the group that took a placebo. However, the researcher fails to realize that the sample size was too small to detect a difference. As a result, the researcher makes a type II error and concludes that the drug is not effective, when in reality it is.

Type II errors can have serious consequences. In the example above, the researcher may decide not to use the drug, even though it could be effective in reducing blood pressure.

There are a number of things that researchers can do to reduce the risk of type II errors. These include:

• Increasing the sample size
• Increasing the power of the test
• Using a more sensitive test
• Accounting for known sources of variability
• By taking these steps, researchers can reduce the risk of making type II errors and ensure that their conclusions are accurate.

t-test : t- test is a statistical term which is used to define the significant difference between two groups, the differences are measured in terms of means of the groups.

Hypothesis testing

• It uses sample data to make inferences about the population.
• It gives tremendous benefits by working on random samples, as it is practically impossible to measure the entire population.
• Hypothesis testing is a procedure that assesses two mutually exclusive theories about the properties of a population.
•  For Hypothesis testing, the two hypotheses are as follows:

1. Null Hypothesis
2. Alternative hypothesis

• There are two errors defined, both are for null hypothesis condition

• Type-I error corresponds to rejecting H0 (Null hypothesis) when H0 is actually true, and a Type-II error corresponds to accepting H0 (Null hypothesis)when H0 is false. Hence four possibilities may arise:

  • The null hypothesis is true but the test rejects it (Type-I error). The probability of making a type I error is α, which is the level of significance you set for your hypothesis test. 
  • The null hypothesis is false but the test accepts it (Type-II error). The probability of making a type II error is β, which depends on the power of the test. 
  • The null hypothesis is true and the test accepts it (correct decision).
  • The null hypothesis is false and test rejects it (correct decision)

Significant difference: Significant differences in statistics means measurable differences.

Given: 

Error Type: Type I error

Experiment done: 100 times

Significant difference: 95 times

To find: alpha level (α) i.e. probability of type I error

Terms:

Formula: Probability = No of favourable outcome/Total no of outcome

Calculation:

Probability= No of favourable outcome/Total no of outcome

Since we want to find the probability of type I error, we will calculate the total number of cases (= 20) and  number of cases in favour of type I error or which not significant (100-95=5)

Probability= No of favourable outcome(in favour of type I error) /Total no of outcome (cases) 

                 = 5/100

                 = 0.05

Hence, The probability of committing a type I error i.e. alpha level was 0.05

Errors In Hypothesis Testing

Type-I error corresponds to rejecting H0 (Null hypothesis) when H0 is actually true, and a Type-II error corresponds to accepting H0 (Null hypothesis)when H0 is false. Hence four possibilities may arise.

1. The null hypothesis is true but the test rejects it (Type-I error).
2. The null hypothesis is false but the test accepts it (Type-II error).
3. The null hypothesis is true and the test accepts it (correct decision).
4. The null hypothesis is false and test rejects it (correct decision)

Important Points

1) Type-I Error:

• In a hypothesis test, a Type-I error occurs when the null hypothesis is rejected when it is in fact true. That is, H0 is wrongly rejected. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug. That is, there is no difference between the two drugs on average.
• A Type-I error would occur if we concluded that the two drugs produced different effects when in fact there was no difference between them. A Type-I error is often considered to be more serious, and therefore more important to avoid than a Type-II error.
• The exact probability of a Type-I error is generally unknown. If we do not reject the null hypothesis, it may still be false (a Type-I error) as the sample may not be big enough to identify the falseness of the null hypothesis (especially if the truth is very close to the hypothesis).

Additional Information

2) Type-II Error

• In a hypothesis test, a Type-II error occurs when the null hypothesis, H0, is not rejected when it is in fact false.
• For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average than the current drug; that is Ho: there is no difference between the two drugs on average.
• A Type-II error would occur if it was concluded that the two drugs produced the same effect, that is, there is no difference between the two drugs on average, when in fact they produced different effects.
• A Type-II error is frequently due to sample sizes being too small.
• The probability of a Type-II error is symbolized by â and written: P (Type-II error) = â (but is generally unknown).
• A Type-II error can also be referred to as an error of the second kind.

​Hence, An investigator commits type I error in testing hypothesis ​when he/she rejects null hypothesis when it is true.

Research is an organized, systematic, and scientific inquiry into a subject to discover facts, theories or to find answers to a problem. It involves several steps including identification of a problem, review of literature, formulation of hypothesis, research design, data collection, analysis, and interpretation, etc.

Hypothesis: The word hypothesis consists of two words, where ‘hypo’ means tentative or subject to verification and ‘thesis’ implies a statement about the solution of a problem. One of the primary functions of a hypothesis is to state a specific relation between two or more variables in such a manner that it is possible to empirically test them.

Characteristics of a Good Hypothesis:

• The hypothesis should be empirically testable: A researcher should take utmost care that his/her hypothesis embodies concepts or variables that have clear empirical correspondence and not concepts or variables that are loaded with moral judgments or values.
• The hypothesis should be simple: The researcher must ensure to state the hypothesis as far as possible in most simple terms so that the same is easily understandable by all concerned. It should not be complex in nature.
• The hypothesis should be specific/objective: No vague terms should be used in the formulation of a hypothesis. It should specifically state the posited relationship between the variables.
• The hypothesis should be conceptually clear: The concepts used in the hypothesis should be clearly defined, not only formally but also, if possible, operationally. The formal definition of the concepts will clarify what a particular concept stands for, while the operational definition will leave no ambiguity about what would constitute the empirical evidence.
• The hypothesis should be related to a body of theory or some theoretical orientation: A hypothesis, if tested, helps to qualify, support, correct or refute an existing theory, only if it is related to some theory or has some theoretical orientation. Thus, the exercise of deriving hypothesis from a body of theory may also lead to a scientific leap into newer areas of knowledge.

The correct answer is - Option 4

Key Points

• (A) A good hypothesis is based on sound reasoning that is consistent with theory or previous research.
  • This emphasizes the importance of forming hypotheses that are grounded in established knowledge and logical reasoning.
  • Ensures the hypothesis is credible and testable within the framework of existing theory.
• (D) Qualitative researchers may develop guiding hypothesis for the proposed research.
  • In qualitative research, hypotheses often guide the study and provide direction, though they may be more flexible and evolving compared to quantitative research.
  • Helps in setting a preliminary focus while allowing for exploration and discovery during the research process.

Additional Information

• (B) A deductive hypothesis is a generalization based on specific observations.
  • This statement is incorrect. A deductive hypothesis works the other way around: it starts with a general theory and tests hypotheses derived from it.
• (C) Tenth grade biology students who are instructed using interactive multimedia achieve at higher level than those who receive regular instruction only is an example of non-directional hypothesis.
  • This statement is incorrect. This is an example of a directional hypothesis because it predicts a specific outcome (higher achievement with interactive multimedia).

Hypothesis testing

It uses sample data to make inferences about the population.

It gives tremendous benefits by working on random samples, as it is practically impossible to measure the entire population.

Hypothesis testing is a procedure that assesses two mutually exclusive theories about the properties of a population.

 For a Hypothesis testing, the two hypotheses are as follows:

1. Null Hypothesis

2. Alternative hypothesis

There are two errors defined, both are for null hypothesis condition

1. Type I error

2. Type II error

Hence from the above table, we can see, the Type II error accepts the null hypothesis when the test fails and thus it should be rejected.